Odense's fellow Danes FC Copenhagen won 2-0 at Shamrock Rovers to end their opponents' bid to become the first Irish team to reach the group stage and Lithuania's interest ended when 10-man BATE Borisov beat Ekranas Panevezys 3-1.
Panathinaikos, seconds away from a win in last week's third qualifying round first leg until Tore Reginiussen's injury-time goal gave Odense a 1-1 draw, fell behind to an Andreas Johansson goal after 12 minutes in a half-empty Olympic stadium.
Jean-Alain Boumsong and Jose Verdu scored either side of half-time to put the Greens in front, only for Espen Ruud to stun the home crowd with an equaliser just before the hour and put visitors Odense ahead on away goals.
Bashkim Kadrii fired Odense in front with a deflected shot 10 minutes from time and a swerving 30-metre effort by Hans Henrik Andreasen completed the misery for the hosts, who will have the added indignity of having to watch arch rivals Olympiakos in the group stage.
Most fans had already left when the visitors had Bernard Mendy sent off in stoppage-time and Antonis Petropoulos headed a consolation as Odense won 5-4 on aggregate.
Panathinaikos, who sold top striker Djibril Cisse to Lazio, are group stage stalwarts who reached the old European Cup final in 1971.
European football's governing body UEFA said on Tuesday it would send teams of experts to Greece to help the country reform its leagues following increased crowd violence at games and a match-fixing scandal.
More than 60 individuals including club officials, players and businessmen are being investigated by the Athens prosecutor in a match-fixing scandal which erupted in June while three club presidents have been imprisoned pending trial. Violence inside and outside stadiums plagued Greek football last season.
FIRST-HALF STORM
FC Copenhagen, who last season became the first Danish club to reach the knockout stages, weathered a first-half storm at Shamrock.
They snatched the lead three minutes before the break when Senegalese striker Dame N'Doye, top scorer in the Danish Superleague last season with 26 goals, scored from the far post following a corner.
In the 73rd minute, N'Doye, who has played for clubs in Qatar, Portugal and Greece, forced Shamrock goalkeeper Ryan Thompson to make a superb save only for Ecuador's Cristian Bolanos to head in the rebound.
Brazilian Renan Bressan scored to put BATE Borisov 2-1 ahead against Erkanas in the 35th minute but was sent off for a second bookable offence five minutes later.
Ekranas had some good chances in the second half but Belarussian club BATE held out and Mikhael Gordeychuk added a third with one minute left.
