A brace either side of half-time from Cheick Diabate gave Mali the win, and secured their highest finish in the tournament since 1972.
It was the second time these two teams had met in the space of 15 days, with Ghana coming out on top in the first, and Mali started like a team determined not to repeat that result.
Two early chances signalled their intent straight away and it was they who took the lead. A short corner found Seydou Keita, whose shot was spilt into the path of Cheick Diabate, who made no mistake.
Diabate then had a chance to turn provider, but opted to shoot instead of passing to his better-placed teammate.
Ghana's Asamoah Gyan then created a chance for Jordan Ayew, but his shot was aimed straight at the keeper.
Ghana thought they had found the equaliser less than ten minutes into the second half when Vorsah's knock down was swept in by Sulley Muntari, but the Inter Milan man was called back for being offside.
Further hopes of an equaliser took a blow just after the hour mark, as Vorsah received a second yellow card for a boot to the gut, resulting in an early bath for the Ghananian.
Mali nearly took full advantage five minutes later through Diabate, but his header from Keita's free kick flew just wide.
Brothers Andre and Jordan Ayew then teamed up for Ghana, exchanging passes before the latter's curling shot went narrowly wide.
A second goal came after a marauding run was followed by a pinpoint pass by full-back Tamboura, allowing Diabate to once again find the back of the net.
Ghana pushed for a goal that would get them back into the game, with Jordan Ayew coming closest when his shot hit the post, but Mali managed to see the game out and finish third in the 2012 Africa Cup of Nations.