AEK beat 1967 champions Celtic 2-1 in a fervent atmosphere in Athens for a 3-2 aggregate win over the Scottish Premier League giants.
It marked the first real blip during the tenure of Brendon Rodgers with the Bhoys after he recently declared his dismay at the lack of transfer funds available to him.
Greek side PAOK held out for a 0-0 draw at Spartak Moscow after edging the Russian outfit 3-2 in the first leg.
Benfica, champions in 1961 and 1962, earned a 2-1 overall win over Fenerbahce after a 1-1 draw in Istanbul and four-time winners Ajax Amsterdam cruised to a 5-2 aggregate defeat of Standard Liege.
The winners of the third-round ties will now move on to the final play-off fixtures before the Group Stage.
Results in full:
Dynamo Kiev 2-0 Slavia Prague (Agg 3-1)
BATE Borisov 1-1 FK Qarabag (Agg 2-1)
Spartak Moscow 0-0 PAOK Salonika (Agg 2-3)
AEK Athens 2-1 Celtic (Agg 3-2)
Dinamo Zagreb 1-1 FC Astana (Agg 3-0)
Fenerbahçe 1-1 Benfica (Agg 1-2)
Ajax 3-0 Standard Liege (Agg 5-2)