The Bordeaux midfielder scored in each half to complete a memorable tournament for Mali, capped by just their second ever win over their western African rivals.
Diabate opened the scoring after 23 minutes and after Ghana had Issac Vorsah sent off in the 64th minute he secured victory 10 minutes from time.
Mali had lost their previous three third-place play-off but after Garra Dembele shot narrowly wide Diabate gave them a lead thanks to his poacher's instinct.
Ghana goalkeeper Adam Larsen failed to hold onto Bakaye Traore's low shot and Diabate was on hand to stab home the loose ball.
Ghana threatened only once before the break to pull the goal back, but Jordan Ayew's 20-yard effort was comfortably held by Oumar Sissoko.
Ghana thought they had levelled eight minutes after the interval when Sulley Muntari lashed in a knock down but he was just caught offside.
The four-time champion's hopes were then dealt a major blow when Vorsah was needlessly booked for the second time when he kicked out at Samba Diakite.
Mali always looked the likely winners thereafter and, while Jordan Ayew curled another effort from the edge of the area just wide, Diabate made the game safe when he prodded in Adama Tamboura's low pass across the six-yard box.