The tournament had gone through nearly five halves of football without a goal after Saturday's two scoreless draws before Emmanuel Agyemang Badu's finely worked strike late in the first half and Albert Adomah's header in the second put Ghana two up.
Congo were inches away from winning after West Bromwich Albion midfielder Yousuf Mulumbu's late shot was clawed away by Ghana goalkeeper Fatawu Dauda.
Meanwhile, South Africa coach Gordon Igesund accused his players of losing their nerve in Saturday's draw with Cape Verde Islands in the opening match of the tournament. Igesund expected better from his players in front of a home crowd in Soweto.
"Not too many of my players came to the party in the first half, which I thought was a total waste of time – and we weren't much better in the second," said Igesund. "Some of the players seemed to freeze when the whistle blew and lost their nerve."
Cape Verde coach Lucio Antunes was thrilled with the result. "We dignified our country today. It is a small country of 500,000 people, but we made them proud and have nothing to fear," he said.
Live, Eurosport, 3.0/6.0