Asante Kotoko new boss Steve Pollack made a winning start to life as head coach of the Porcupine Warriors but had to bench experienced Awal Mohammed and Felix Annan for the victory.
Baba sent home a sublime touch from the edge of the box after a corner kick taken by Emmanuel Gymafi.
The corner kick was initially headed away by a Tema Youth defender. Before the ball could go out of the goal area completely, Baba Mahama stopped it.
The goal gave the dominant Kotoko fans at the Park great relief while serving as a deserved reward for the Porcupines, whose relentless fight for victory was evident from the beginning.
That victory will give confidence to new boss Steve Pollack who made a hard call of dropping both Felix Annan and defender Awal Mohammed.
Goalkeeper Ernest Sowah will now fancy his chance of making it in the second half of the season after a difficult first half of the season where Felix was the undisputed number one.