Lazio posted a dazzling 4-0 victory at Levski Sofia for their first win in Europa League Group G.
Beaten by Red Bull Salzburg in their opening pool game and struggling in Serie A, the Italian side produced a much-improved play against a toothless Levski at the Georgi Asparuchov Stadium.
After a tight start, Matuzalem opened the scoring midway through the first half before Mauro Zarate added the second on the stroke of half-time.
Second-half goals from Mourad Meghni and Tommaso Rocchi crowned a fine win for the Rome outfit.
In the same pool, Salzburg's dream start to the competition continued as they claimed the prized scalp of Villarreal with a 2-0 home win thanks to goals in either half from Marc Janko and Somen Tchoyi.
Everton shrugged off the loss of 10 first-team players to record a superb 2-1 victory at BATE Borisov in Group I thanks to Tim Cahill's goal 13 minutes from time.
In the process, David Moyes' side have taken a massive step towards securing a place in the next stage after their second successive group win. Cahill capped a brilliant comeback after Marouane Fellaini had cancelled out Dmitri Likhtarovich's opener to haul the Toffees level in the 68th minute.
AEK Athens bounced back from their thrashing at the hands of Everton a fortnight ago as they edged out Benfica 1-0 in the Greek capital tonight. Daniel Majstorovic's strike two minutes before the break was the difference.
Werder Bremen moved three points clear at the top of Group L after seeing off Athletic Bilbao 3-1 despite losing Peter Niemeyer to a red card just five minutes after he appeared as a second-half substitute.
The German side led 2-0 at the break thanks to a brilliant volley from Aaron Hunt and a well-worked effort from defender Naldo, and although Fernando Llorente pulled a late goal back for Athletic, it was not enough for the visitors and they conceded a third almost immediately when Torsten Frings slotted home from the penalty spot.
Austria Vienna had to settle for a point in their Group L clash with Portuguese side Nacional. Milenko Acimovic missed a penalty 10 minutes into the game for the hosts and Ruben Micael gave the Madeirans the lead after 35 minutes. An away win looked on the cards until Brazil-born Schumacher tied the game in the 76th minute.
Last season's UEFA Cup champions Shakhtar Donetsk took control of Group J with a 4-1 victory over Partizan Belgrade. Two goals in each half, with Luiz Adriano, Jadson and Yaroslav Rakitskiy adding to Marko Lomic's 24th-minute own-goal, ensured victory before a late consolation from Adem Ljajic.
Also in the pool, Ivan Perisic's stoppage-time equaliser gave Club Brugge a 2-2 draw at Toulouse. Joseph Akpala put the Belgian side ahead seven minutes into the second half but their lead lasted just two minutes before Moussa Sissoko celebrated getting his second France call-up today with the equaliser.
It looked as though Andre-Pierre Gignac's 84th-minute goal would hand all three points to Toulouse but Perisic levelled in the dying seconds.
Senegalese striker Dame Ndoye's first-half goal proved the difference as FC Copenhagen recorded a 1-0 home win over Sparta Prague in Group K. Otman Bakkal's first-half header was enough for PSV Eindhoven to claim their opening win of this year's competition at home to CFR Cluj in the same pool.
In Group H, Alex scored the only goal as Fenerbahce bounced back from their opening Europa League defeat to FC Twente with a 1-0 win at Sheriff Tiraspol in a low-key encounter. Steve McClaren's Twente, meanwhile, were held to a disappointing goalless home draw by Steaua Bucharest.
Los Che fell behind to a Sergio Floccari, but stormed out of the blocks in the second half and quickfire goals from David Silva and Nikola Zigic put them in front. Houssine Kharja drew the Italian side level from the penalty spot but the match was finally settled when David Villa was tripped in the box with 10 minutes left and applied the finish from 12 yards.
Lille also came from behind to thrash Slavia. Tjani Belaid's early penalty had the French side on the back foot, but they were back on level terms when Marek Suchy turned the ball into his own net early in the second half.
Pierre Alain-Frau then put them ahead with 20 minutes to go before the floodgates opened in the dying stages. Gervinho got the third with five minutes to go and Arnaud Souquet added another before Gervinho grabbed the fifth.
Claudio Ranieri got the result he was after from his Roma players after they ended a run of disappointing results with a 2-0 victory over CSKA Sofia in Group E. The win was secured with two goals in three first-half minutes from Stefano Okaka Chuka and Simone Perrotta.
In the same pool, Danny Murphy's 57th-minute winner saw Fulham sink Basle to halt their three-match losing streak and surge to the top of the standings.
Jonathan Legear's late equaliser maintained Anderlecht's unbeaten start to Group A and denied Martin Jol's Ajax their first pool win this evening. The game at the Constant Vanden Stock Stadion had looked to be heading for a goalless draw until substitute Dennis Rommedahl broke the deadlock 18 minutes from time.
Jelle Van Damme was dismissed in the 82nd minute, but the hosts made light of their man disadvantage and nicked a 1-1 draw through Legear four minutes later.
Anderlecht remained top of the pool, a point clear of Dinamo Zagreb who were 3-0 winners at FC Timisoara. Milan Badelj was the star of the show, scoring the first goal and laying on the other two for Jorge Sammir and Pedro Morales.
In Group C, Hamburg got their campaign up and running with a 4-2 win over Hapoel Tel Aviv. Two goals in the first 12 minutes from Marcus Berg had them in control but substitute Itay Shechter pulled the Israeli side back into the game.
Eljero Elia made it 3-1 only for Samuel Yeboah to reduce the deficit again. Ze Roberto missed a penalty for the German side just before the midway point in the second half - but then found the target to make sure of the victory.
Celtic, meanwhile, were held 1-1 by old foes Rapid Vienna at Parkhead. The home side were shocked to lose a goal to Nikica Jelavic after only three minutes but recovered to level in the 20th minute through Scott McDonald.
Panathinaikos midfielder Giorgos Karagounis decided an underwhelming Group F match against Dinamo Bucharest with a late strike in front of an empty Stadion Dinamo. Dinamo had been ordered to play the match behind closed doors after the crowd trouble that forced the abandonment of their play-off against Liberec earlier in the competition.
Also in Group F, Sturm Graz fought hard to hold favourites Galatasaray to a 1-1 draw in Turkey. Daniel Beichler gave the Austrians the lead in first-half stoppage-time but Frank Rijkaard's Gala levelled through Milan Baros in the 63rd minute.
In Group D, a superb second-half rearguard earned Latvian champions FK Ventspils a point at home to Heerenveen.
Sporting Lisbon's Adrien Silva had an eventful evening, scoring the game's only goal in the 19th minute and then being sent off in stoppage time against Hertha Berlin.