Wakaso scored from the spot in the first half after Emmanuel Agyemang Badu had been brought down in the area at the Nelson Mandela Bay Stadium.
However, the midfielder could find himself in trouble with FIFA after celebrating by pulling his shirt over his head to reveal a T-shirt with the words "Allah is Great!"
Wakaso was shown a yellow card for his celebration, ruling him out of Ghana's final group game, and could face further sanctions as FIFA rules prohibit players from making religious or political statements during a game.
In a first half low on clear-cut chances, referee Noumandiez Doue was the central figure and was faced with a number of big decisions.
The first came after just seven minutes when goalkeeper Ghana goalkeeper Fatau Dauda handled the ball outside the penalty area as defender John Boye attempted to shield the ball back to him with Seydou Keita lurking.
However, the referee produced only a yellow card - much to Keita's annoyance - and the same player then curled the resulting free-kick narrowly wide of the post to compound his fury.
Ghana eventually settled and Badu saw his header catch the outside of the post after he had done well to get on the end of a free-kick from Wakaso, who had slipped as he played the ball in.
And just four minutes later Ghana took the lead following another major decision for the referee.
Asamoah Gyan attempted to find Badu in the area and he was brought down by Adama Tamboura, although replays suggested Tamboura had initially connected with the ball as he slid in.
Doue pointed to the spot and Wakaso calmly stroked the spot-kick home, even though goalkeeper Mamadou Samassa went the right way.
Mali had beaten Niger in their opening group game but looked short of ideas and never seriously threatened to get back into the contest in a poor second half which featured more yellow cards than chances.
Ghana attempted to increase their lead and Gyan shot narrowly wide before Badu saw a free-kick pushed wide by Samassa, while substitute Solomon Asante also flashed a shot the wrong side of the post in the closing stages.