The decisive goal at the Nelson Mandela Bay Stadium came when Mali defender Adama Tamboura needlessly bundled over Emmanuel Agyemang Badu in the area to concede a penalty which Mubarak Wakaso swept home in the 38th minute with an emphatic spotkick.
The youngster was then immediately booked, however, for displaying a religious slogan when he lifted up his jersey to reveal "Allah is Great" emblazoned on his t-shirt.
It was his second yellow of the tournament and he will now miss Ghana's third group match against Niger on Monday.
Ghana, who also hit the woodwork in the first half with a header from Agyemang Badu, are top, a point clear of Mali. Democratic Republic of Congo, who have one point, and Niger, who have none, meet at 1800GMT.