Veteran Asamoah Gyan scored what proved to be the game's only goal after 22 minutes to lead his side to yet another AFCON knockout stage, a feat Ghana has achieved in all editions since 2008.
Minutes later Mali had its first chance, when defender Molla Wague jumped higher than his markers, but his header went over the crossbar.
The Black Stars took the lead two minutes after. Jordan Ayew received a long ball on the right side, before finding captain Gyan inside the vital area, and the latter's header went in with Mali's goalkeeper Oumar Sissoko completely beaten.
The opening half witnessed no further chances, with Ghana looking dangerous every time Atsu had the ball.
Mali started the second half throwing everything in attack trying in search of the equalizer. Lanky striker Moussa Marega missed a couple of clear cut chances in a spate of two minutes.
Firstly, he saw his header from six yards from a Bakary Sako cross saved by Ghana goalkeeper Razak Brimah five minutes after the break. Two minutes later, he was the first to reach a loose ball from Sako but his effort was off target.
Mali continued to press and five minutes later defender Salif Coulibaly fired a long range shot that went just wide.
Malian substitute Khalifa Coulibaly could have rewarded his coach a few seconds after his inception, when he was the first to meet Moussa Doumbia’s cross from the left side, but his header was cleared off the line by Daniel Amartey ten minutes from time.
Ghana survived another late double scare when substitute Yves Bissouma rounded his marker two minutes from time, but his cross went without a follower.
Deep into the injury time Coulibaly thought he had grabbed a very late equalizer when he fired a thunderous ball, but for Brimah to produce a fine save as the game ended with Ghana guaranteeing their quarter final ticket.
Total Man of the Match
Thomas Partey (Ghana)
Avram Grant (Head Coach, Ghana)
I'm happy for the win and I thank my boys for showing maturity especially in the second half. We didn't plan to sit back in the second half. In tournaments like this you need to collect points and that's what we did. In the first half we scored and missed many chances but we had to secure our victory in the second half. Mali played a physical game but I used my normal tactic and we won. We have six points and we played a good game. Baba Rahman sent us a touching message before the game and we wish him speedy recovery. We just wanted to qualify and I don't want to speak about the pitch again.
Alain Giresse (Head Coach, Mali)
Every coach is responsible for his team's results. The defeat today is my fault and I take full responsibility. Lassana Coulibaly didn't play because I changed the tactic and thought he should be left on the bench. My players don't have a confidence problem but most of them lack experience. Today, it was easy to produce a very young team but that was to be a risk against a team like Ghana. I know they will get the needed experience with time. We had many chances to score in the second half but we couldn't. It's not a matter of training because training differs from matches. Ghana scored and that's what made the difference. My players should raise their heads high and think of the coming game.