Former Sunderland striker Asamoah Gyan headed the only goal in the 21st minute against Mali.
The Black Stars had already beaten Uganda 1-0 in their Group D opening match and have qualified for the last eight regardless of the result in their final group match against Egypt on Wednesday.
"In tournaments like this victories are more important than beautiful football," said Grant, responding to criticism about the team’s perceived lack of style.
Grant, whose contract expires after the tournament, will be hoping to go one better than 2015 when he took Ghana to the finals before losing to the Ivory Coast on penalties.
