Panathinaikos go through
With the tie level 2-2 from the first leg, The Greek side took the lead two minutes into the match in Athens through Greek international defender Panagiotis Fyssas.
His goal would be the only one of the night as Liberec could not find the needed two goals to overturn the tie.
The Greek giants will go into the draw for the competition's round of 16, which will be played early next year.
AEK Athens continued to show their great form in the competition, following up a 4-0 win at home to Maccabi Haifi in the first leg - with a 4-1 win against the Israelis in the second game.
The Greek side were never in danger of losing the tie, but with Maccabi playing for pride they nonetheless kept their concentration.
Walid Badir grabbed an opener for the Israeli side with a fourth minute penalty, but goals from Kostas Katsouranis and Vasilis Lakis ended any hope of a miraculous come-back.
With the match entering the final minutes, Maccabi heads dropped and they conceded twice more - through Lakis again and Dimitris Nalitzis to lose the tie 8-1 on aggregate.
Czech Republic side Slavia Prague emphatically overturned a 1-0 first leg deficit to beat Greek side PAOK Salonika 4-0 in the second leg, going through 4-1 on aggregate.
Goals by Rudolf Skacel, Stepan Vachousek and a late brace by Pavel Kuka were enough to dump the Greek side out of Europe for this season.
German side Stuttgart got a late Aliaksandr Hleb goal in injury time at the end of the match to beat Club Brugge 1-0 in the second leg and 3-1 on aggregate.
Die Bundesliga side had a 2-1 first leg lead against their Belgian counterparts and were able to hold in return leg at the Gottlieb-Daimler-Stadion.
Click below for match stats:
Uefa Cup - third round, second leg
Maccabi Haifa 4-1 AEK Athens (AGG: 8-1)
Panathinaikos 1-0 Slovan Liberec (AGG: 3-2)
Slavia Prague 4-0 PAOK Salonika (AGG: 4-1)
Stuttgart 1-0 Club Brugge (AGG: 3-1)
