Ghana went ahead on 13 minutes as Madi Panandetiguiri was ruled to have pulled down Christian Atsu as the pair challenged in the area. Wakaso did not lose concentration amid the fierce protests of the Burkina Faso defence, duly slotting a fine penalty kick low into the right corner. It was Wakaso's fourth goal of the tournament - and third from the penalty spot.
Asamoah Gyan should have made it 2-0 on 58 minutes when he tried to steer home Atsu's cross on the run but his effort came back off the right-hand post. Gyan's miss looked costly two minutes later as Burkina Faso levelled. Agyemang-Badu was robbed of possession in midfield and the ball was fed to Bance, who found a huge gap between the centre-backs and had time to pick his spot.
The last chance for either team in normal time came on 84 minutes when Atsu fired in an effort from the edge of the area but Daouda Diakite got down to save.
In extra time, the Burkinabe spurned a chance in the 99th minute when Kone headed over the bar from Kabore's corner while unmarked six yards out. Gyan flashed a header wide in the 119th minute as Ghana's final chance went away.
But it was Burkina Faso who finished on the front foot, Bance's turn and shot deflected over the bar in the last meaningful attack as the lottery of penalties was required to settle a breathless encounter. However they were hit by a late set-back as star midfielder Jonathan Pitroipa was sent off for a second yellow card.
Another poor effort by Emmanuel Clottey put Ghana in even more trouble, and with Burkina Faso netting through Bakary Kone, Henri Traore and Bance, the shoot-out was settled when Emmanuel Agyemang-Badu's effort was saved by Diakite.