Marcus Brown drove through an inexplicable hole to lay-up the winning basket with just 1.2 seconds left to secure the victory for Malaga.
Brown was super down the stretch as he scored 12 of his 14 points in the final six minutes while Mark Tusek was five from six from three point land as he had 18 points.
Igor Rakocevic finished with 16 points for TAU but 14 of them came in the first half, Luis Scola also had 14 points but was only 50% from the field as he produced another erratic performance.
Malaga looked a little too reliant on outside shooting in the first half and TAU were having more joy in the paint, they had a nice 11-2 run at the end of the half which saw them go into the dressing room 40-35 in front.
The streaky nature of the match continued in the third quarter, Unicaja did remarkably well to level matters at 49-49 before their offense shut down once more allowing TAU to go on a 9-0 run.
The Basques would lead 61-51 at the end of the third quarter but Malaga gradually worked their way back into things and with 1 minute and 20 seconds left a three pointer from Brown gave them the lead for the first time in the half.
Both sides started to exchange baskets then, and when Pablo Prigioni snuck in for a lay-up with 8.4 seconds left they were back level at 74-74.
Malaga set up for the final attack and TAU got their wires crossed on defense as Brown was able to dribble into paint unchallenged and lay-up the winning basket.