Larissa, who found themselves going into their match against AEK in outright 5th place and on a nine match unbeaten run, did their best to impose themselves in the opening stages at the Alkazar.
Save for an early effort from Stelios Venetidis they found their opponents typically difficult to break down, a trait that has characterized Bajevic's campaign this season.
In fact it was AEK who came closest to scoring with two Nacho Scocco efforts during the first half, the second of which was cleared off the line by Panagiotios Katsiaros.
Though both sides emerged for the second half with a clear intent to attack each other, it wasn't until the final minutes of normal time that a fairly even encounter exploded dramatically into action.
Larissa took an 89th minute lead through a brilliant long-range strike by Giorgios Fotakis, the midfielder curling his effort into the top left-hand corner of Sebastian Saja's net.
However, AEK responded just over a minute later through Rafik Djebbour.
The Algerian striker started the match up front for the Athenians despite having been a doubt through illness and produced a tidy low finish from Gustavo Manduca's superb run and cut-back in the first minute of injury-time, securing for his side a crucial victory as they chase European football next season.
