Udinese's Antonio Di Natale masterminded a second-half fightback as Liverpool went down to a 3-2 defeat at Anfield.
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The Reds looked to be on course for victory when they took the lead through Jonjo Shelvey after 23 minutes but dangerman Di Natale equalised just 35 seconds into the second-half.
The Udinese captain then swung in a free-kick that Sebastian Coates nodded into his own net, and the Italians completed an impressive turnaround two minutes later when Di Natale released Giovanni Pasquale, whose stunning 25-yard strike beat Pepe Reina.
Substitute Luis Suarez pulled one back for Liverpool, and both he and Raheem Sterling had chances to snatch a point, but the Reds were left to rue a host of wasted chances as they suffered a sobering defeat.
Two goals from Samuel Eto'o earned Anzhi Makhachkala a 2-0 victory over Young Boys. Cameroon international Eto'o struck twice in the second half to inflict a second successive defeat on their Swiss opponents.
Anzhi had played out a 1-1 draw with Udinese in their Group A opener, while Young Boys were beaten by Liverpool in an eight-goal thriller.
Panathinaikos scored a late equaliser as they held Tottenham Hotspur to a 1-1 draw in Group J.
Michael Dawson, who has found first-team opportunities hard to come by under new manager Andre Villas-Boas, but the defender made the most of his recall in the first half by glancing home a Tom Huddlestone cross to put Spurs ahead.
The England centre-half was then at fault for the Panathinaikos equaliser in the second half, though, as he was outpaced by striker Toche, who beat Hugo Lloris after a brilliant through-ball from Giourkas Seitaridis.
Honorato Ederson earned Lazio their first win in Group J after his second-half strike saw them defeat ten-man Maribor 1-0 at Rome's Stadio Olimpico.
Both sides struggled to impose themselves in the first half before Ederson broke the deadlock in the 62nd minute with a low strike past Maribor keeper Jasmin Handanovic. Maribor were then reduced to ten men when Jovan Vidovic was dismissed for a foul on Sergio Floccari in the area, with Anderson Hernanes unable to double Lazio's lead from the resulting penalty thanks to a fantastic save by Handanovic.
Newcastle leapfrogged Bordeaux at the top of Group D with a comfortable 3-0 win over the French side.
Shola Ameobi put the Magpies in front after 16 minutes after good work down the left from Gabriel Obertan. Newcastle were gifted a second after Henrique diverted Danny Simpson's cross into his own net, and Papiss Cisse appeared to be offside when he swept home Shane Ferguson's cross for the third.
Second-half goals from Carlos Bacca and Bjorn Vleminckx helped Club Brugge, beaten by Bordeaux in their opener, to a 2-0 win over Maritimo.
Maritimo looked formidable opponents early on and Rodrigo Antonio do Nascimento struck the bar just after the half hour mark before a fine individual goal from Bacca and Vleminckx's simple finish sealed victory for Brugge.
Inter Milan eased to a 3-1 away win over Azerbaijan's Neftchi to move to four points from two Group H matches.
Inter kicked off their campaign by salvaging a last-gasp home draw against Rubin Kazan but were back to winning ways against their Azerbaijani opponents.
Philippe Coutinho opened the scoring after ten minutes with Joel Obi and Marko Livaja adding to the first-half lead before Nicolas Canales scored the hosts' consolation eight minutes after the restart.
In Group H's other game, two strikes either side of half-time gave Rubin Kazan a 2-0 victory over Partizan Belgrade and kept their magnificent home record in European competition intact.
Gokdeniz Karadeniz opened the scoring just before the interval, although Partizan Belgrade had looked the better team up until that point, before Alexander Ryazantsev sealed the points within three minutes of the re-start.
Cristian Rodriguez struck deep into stoppage time to continue Atletico Madrid's remarkable European run of 14 consecutive victories as they eventually saw off a brave challenge from Viktoria Plzen to win 1-0.
The Czech side had successfully stifled last season's winners throughout and could even have gone ahead themselves when Vaclav Prochazka's brilliant free-kick forced Sergio Asenjo into a fabulous save just before the hour mark.
However, Atletico continued to probe until the final whistle and finally got their reward when Rodriguez received the ball on the edge of the area and gave Matus Kozacik no chance with a sweetly-struck volley - his first goal for the club since joining from Porto.
Omer Damari's stoppage-time equaliser for Hapoel Tel-Aviv ended Academica's hopes of their first European win in more than 40 years as the teams drew 1-1 in Coimbra.
Salim Cisse looked to have earned the Portuguese side their first win in European competition since their 2-0 victory over FC Magdeburg in 1969 when he scored from close range just after the break. However, Damari ruined the celebrations when he levelled the scores in the last action of the game with a header from the middle of the area.
Loic Remy scored twice as Marseille returned to form in fine style with a 5-1 win over Cypriot opponents AEL in their Group C clash at the Stade Velodrome.
The Ligue 1 leaders headed into the game reeling from their first loss in 13 matches on Sunday, when they crashed 4-1 at domestic rivals Valenciennes, and Elie Baup's men were braced for further embarrassment when Edwin Ouon put the visitors in front after 22 minutes.
However, Rod Fanni equalised three minutes before the break before Lucas Mendes, Andre Gignac and Remy's brace secured the win.
Raul Meireles and Dirk Kuyt got on the scoresheet as Fenerbahce heaped more woe on Borussia Monchengladbach with a solid 4-2 win in Group C.
The Turkish side, who had started their campaign by drawing with Marseille two weeks ago, hit back from Luuk De Jong's early opener for the Germans, who have now gone seven games without a win.
Athletic Bilbao's miserable start to the season continued as last year's finalists were beaten 3-1 by Sparta Prague.
Tomas Zapotocny's powerfully driven shot went straight through Gorka Iraizoz to give the hosts the lead on 25 minutes and the Czech side were somewhat fortunate to double their lead before half-time when Bekim Balaj's header took a wicked deflection off Aritz Aduriz on its way into the bottom corner.
Sparta got another slice of luck when a penalty was awarded for Xabier Castillo's challenge on Vaclav Kadlec despite the contact appearing to take place just outside the area, and Josef Husbauer calmly slotted away the penalty.
Oscar de Marcos pulled a goal back for the visitors with 20 minutes remaining.
Yassine Benzia struck in injury-time to snatch a 4-3 win for Lyon and deny Hapoel Kiryat Shmona a deserved point in a thrilling encounter.
Les Gones trailed to Shimon Abuhatzira's early goal but then put themselves in the driving seat thanks to Gueida Fofana, Fabian Monzon and Anthony Reveillere.
Kiryat Shmona hit back after the interval, however, through Lior Levi and a Abuhatzira penalty and they looked to have secured a draw until Benzia's late heroics.
PSV Eindhoven got their campaign back on track with an impressive 3-0 victory at home to Napoli at the Philips Stadion.
Goals from Jeremain Lens, Dries Mertens and Antonio Marcelo lifted the Dutch side to a one-sided win as they bounced back in style from defeat to FC Dnipro in their Group F opener.
Second half-strikes from Vitaliy Mandziuk and Yevhen Seleznyov saw Dnipro come from behind to beat AIK 3-2 and go top of Group F.
After opening their campaign with a 2-0 success over PSV, the Ukrainian side registered a second victory despite going in 2-1 behind at the break. Helgi Danielsson put the Swedes in front in the fourth minute before Nikola Kalinic and Henok Goitom traded goals just before interval.
Dnipro hit back strongly in the second period and found their reward through Manziuk's 75th-minute leveller and Seleznyov's winning effort seven minutes from time.
Videoton got up and running in Europa League Group G with a 3-0 home victory over Sporting in Szekesfehervar.
First-half goals from Paulo Vinicius, Filipe Oliveira and Nermanja Nikolic put the hosts in control at Sostol Stadion, and there was no way back for Ricardo Sa Pinto's visitors.
A second-half double from captain Marco Streller rescued a 2-2 draw for Basel against Genk.
Benjamin De Ceulaer and Jelle Vossen put the visitors two up at the break and looked set to record their second consecutive group win.
However, Streller reduced the deficit after 71 minutes from the spot before equalising with five minutes left as Basel picked up their second draw of the group stage.
Hannover came back from a goal behind and a man down in the opening ten minutes to beat defeat Group L rivals Levante 2-1.
Karim Haggui was dismissed for denying a clear goalscoring opportunity when he brought down Theofanis Gekas and Michel slotted away the resultant penalty after just nine minutes. However, the German side would not lie down and were deservedly level when Szabolcs Huszti also scored from the penalty spot after Vicente Iborra had been penalised for handball.
Didier Konan's finish from close range four minutes into the second-half was then enough to give last season's Europa League quarter-finalists all three points as they moved to the top of the standings.
Hosts Helsingborg threw away a two goal lead as FC Twente came from behind to snatch a 2-2 draw.
Nikola Djurdjic opened the scoring for the home side in the seventh minute with a well-taken header before he doubled the Swedish champions' lead two minutes before the break.
Rasmus Bengtsson pulled one back for Steve McClaren's side in the 74th minute before Douglas levelled the score with two minutes left on the clock to deny the Swede's their first win in Group L.
Bayer Leverkusen picked up their first win in Group K as they saw off Rosenborg 1-0.
Substitute Stefan Kiessling scored the winning goal a minute after entering the action with quarter of an hour remaining, the striker firing home on the rebound after Rosenborg's goalkeeper failed to hold on to Sidney Sam's low cross.
Junior Fernandes and Gonzalo Castro both hit the woodwork for the visitors as Leverkusen emerged as deserved winners in Trondheim.
Ukrainians Metalist extended their unbeaten start in Europa League Group K with a battling 2-0 win over Rapid Vienna in Kharkiv.
Second-half goals from Edmar and Cleiton Xavier capped a dominant performance by the hosts, who had began their group campaign with a goalless draw against Leverkusen in Germany.
Stefan Nikolic earned Steaua Bucharest their first win in Group E as they beat FC Copenhagen 1-0.
The substitute striker headed the Romanian side ahead in the 83rd minute in a game lacking any other real clear cut chances to extend his side's unbeaten run in group stage home games to eight - four wins and four draws.
In the same group, Molde picked up their first victory as they beat Stuttgart 2-0.
Second-half strikes from Jo Inge Berget and Daniel Chukwa were enough for the victory as the Norwegians moved above their German opponents in the table.