Forward Cheick Diabate scored both goals for the Eagles as defender Isaac Vorsah saw red for a second bookable offence to leave the Black Stars with 10 men on the pitch.
The Malians took the lead two minutes later when Diabate scored from close range after Ghana goalkeeper Adam Kwarasey had spilled a resulting shot off a corner kick.
The Eagles began to dominate the game.
Their dominance was rewarded on 80 minutes when full-back Adama Tamboura's inch-perfect cross from the left was tapped in by Diabate for the Eagles' second goal.
The win avenged Mali's first-round loss to Ghana as they secured their first Africa Cup of Nations medal since 1972, when they finished second.
