Mario Haas was the injury-time hero for Sturm Graz as they found two late goals to see off an AEK side, who had survived all but nine second-half minutes with 10 men, 2-1.
The Greek side had taken control of their Group L match with Joachim Standfest's own-goal in the 51st minute, only to see Trainos Dellas pick up two yellow cards in quick succession and leaving the field three minutes later.
Sturm looked like they would not be able to make their numerical advantage count until Thomas Burgstaller's levelled in the 87th minute, leaving the path clear for Haas to drive home the winner in added time.
Veteran striker Eidur Gudjohnsen looked up for the match in the opening exchanges, twice finding space to shoot in the first five minutes, both times drawing saves from Silvije Cavlina in the Sturm goal.
The Austrians looked overwhelmed in the first 15 minutes, with Roger and Steve Leo also pouring forward and letting fly on goal.
The visitors eventually found a foothold in the game and were not unduly perturbed by the enforced departure of Haris Bukwa, who was taken off with an injury in the 40th minute.
As the interval approached Fabian Vargas and Leonardo both wasted chances to send the hosts in ahead.
Dellas received his first yellow card five minutes after the restart for a poor challenge but moments later his side were in front.
Jose Carlos and Leonardo were involved in the build-up but it was left to Sturm defender Standfest to apply the final touch, inadvertently heading the ball past his own goalkeeper.
The home side only had three minutes to enjoy their lead before Dellas handballed and earned a second caution, forcing an immediate reshuffle.
Roger was sacrificed for an extra defender, in Mavroudis Bougaidis, and AEK managed to to stifle their opponents for an extended period.
Their own attacking ambition was shelved as they instead tried to sit on their advantage and with Graz struggling to find the gaps, it looked likely to yield three points.
Burgstaller went close with a header eight minutes from time and then succeeded in claiming the equaliser with three minutes left in normal time.
Standfest was the provider at the right end this time and Burgstaller stabbed home.
That gave the visitors renewed hope and in the second minute of added time Imre found Haas, who found the target from 18 yards to seal a dramatic win.