UEFA Cup winners Shakhtar Donetsk are out of the Champions League on away goals after being held to a goaless draw at Politehnica Timisoara.
The Romanian outfit progressed thanks to a 2-2 first leg result in Ukraine.
Slavia Prague follow them into the Europa League after drawing 1-1 at home to Sheriff Tiraspol in the other shock of the night.
The first leg in Moldova had finished goaless and it looked like things were going to plan for Slavia when Adam Hlousek scored in the 15th minute.
But Jose Nadson pounced in the fourth minute of stoppage time to send Sheriff through on away goals.
BATE Borisov faced the heartache of going out on away goals despite beating FK Ventspils 2-1 on the night.
Trailing from the first leg, the hosts faced an uphill struggle from the off and their task grew tougher when Igor Tigirlas put Ventspils in front in the 14th minute.
Sergey Krivets scored either side of the break to give Bate hope but they could not find the vital third goal.
A last-gasp goal saw Celtic overcome a first-leg deficit to battle past Dinamo Moscow 2-1 on aggregate, winning 2-0 on the night.
The Hoops had never won a European tie after losing the first game at Parkhead but Scott McDonald's header a minute from the break in the Arena Khimki levelled the tie 1-1 on aggregate.
The game looked to be heading for extra-time but in the final minute a sensational goal by substitute Georgios Samaras, on for McDonald, sent the Parkhead side into the Champions League play-offs and ended a six-year drought on their European travels.
Levski Sofia are through thanks to a 2-0 defeat of FK Baku, after the first leg ended goaless.
Hristo Yovov put the Bulgarian champions ahead in the 64th minute and former Baku striker Georgi Hristov sealed the result 10 minutes from time.
Hungarian champions Debrecen's 1-0 triumph against Levadia was enough to see them through after a win by the same score in Tallinn last week.
Adamo Coulibaly scored the only goal of the game in the 70th minute.
After being beaten 3-2 at home, FC Zurich made easy work of the second leg, comfortably seeing off NK Maribor 3-0.
Dusan Djuric opened the scoring in the 21st minute and Xavier Margairaz doubled the visitors' lead on the stroke of half time before Adrian Nikci sealed the result in the 76th minute.
Olympiacos repeated their success in Slovakia by defeating Slovan Bratislava 2-0 again.
Enzo Maresca netted in the 35th minute and substitute Diogo nabbed the second shortly before the hour mark.
Apoel Nicosia survived an early scare at Partizan Belgrade to go through 2-1 on aggregate.
The hosts took an early lead thanks to Almani Moreira's third minute goal but the Cypriot side held out for the rest of the match.
Elsewhere, FC Copenhagen are through 3-1 on aggregate following a goaless draw at Stabaek.