The Al Ain striker and Andre Ayew scored in the Black Stars' second Group D win, while Guinea thrashed Botswana to keep their cup hopes alive.
Asamoah Gyan scores and Ghana on the brink of the quarter-finals
Ghana moved to the brink of a place in the quarter-finals of the African Nations Cup with victory over Mali in Franceville.
Goals from Asamoah Gyan, the Al Ain striker, and Andre Ayew gave the Black Stars a second win in as many Group D games, with a game against fellow qualifying hopefuls Guinea to come in the final round.
However, the outcome could have been so different had Mali striker Cheick Diabate not seen his free-kick strike both posts when the game was goalless.
Mali started brightly, with Sochaux forward Modibo Maiga showing why he has attracted interest from European sides with some enterprising wing play.
In the 21st minute Ghana defender John Boye was lucky to escape punishment for making contact with his studs with Ousmane Berthe while the Mali defender was on the ground.
However, Ghana gradually began to assert themselves on the contest and the first chance of the game came soon after, in the 25th minute, when Kwadwo Asamoah’s left foot shot from long range brought a fumbled save out of Soumaila Diakite - and Sulley Muntari was unable to turn the rebound in.
Asamoah produced another powerful left-foot shot 10 minutes later - but his effort went wide.
However, Ghana had a lucky break in the 38th minute when Diabate saw his 20-yard set-piece strike both posts. The rebound fell to Abdou Traore - but he fired over.
The last chance of the first half came when Ayew rose highest to meet Emmanuel Agyemang-Badu’s centre - but his header went wide.
Diakite saved low from Ayew in the 55th minute and reacted sharply to deny the Marseille striker another chance on the follow-up.
However, Ghana opened the scoring after Bakaye Traore fouled Ayew, with Gyan curling his 63rd-minute free-kick expertly into the top corner of the goal.
And Gyan had a hand in Ghana’s second goal, 13 minutes later. The striker, on loan with Al Ain from the Premier League club Sunderland, found Ayew with a clever backheel and watched as his team-mate cut inside and beat Diakite at his near post with a low left foot shot from 12 yards.
In the night's second Group D game Guinea kept alive their African Nations Cup hopes, at Botswana's expense, with a thumping victory.
A Sadio Diallo brace and strikes by Abdoul Camara, Ibrahima Traore, Mamadou Bah and Naby Soumah secured a one-sided triumph that will give Guinea renewed hope and confidence heading into their final group game with Ghana on Wednesday.
Dipsy Selolwane claimed Botswana's reply from the penalty spot but the Zebras were as good as out of the match by half-time, trailing 4-1 and reduced to 10 men following the dismissal of Patrick Motsepe for a potentially leg-breaking challenge on Pascal Feindouno.
Both these teams lost their opening matches, Botswana beaten 1-0 by Ghana and Guinea losing to Mali by the same scoreline. Botswana striker Jerome Ramathlakwana labelled the match "do-or-die" affair before kick-off, and ultimately it was his side left to face up to almost certain elimination.