Emmanuel Clottey and Isaac Vorsah also missed for the 10-man Black Stars, while Paul Kebe Koulibaly failed from the spot for Burkina Faso.
Mubarak Wakaso’s penalty gave Ghaman the lead, but the outstanding Aristides Banse drew his side level.
Burkina Faso started the brighter and Jonathan Pitroipa had claims for an early penalty when he was bundled over by John Boye inside the sixth minute.
Ghana took the lead on 13 minutes when Wakaso slotted home from the spot after Mady Panandétiguiri was adjudged to have fouled Christian Atsu.
The Black Stars were always dangerous on the break, with skipper and former Sunderland man Asamoah Gyan denied by Diakite on the half-hour.
Solomon Asante spurned a glorious chance to double Ghana’s lead six minutes before the half, but Lyon’s Bakary Kone managed to divert it above the bar and for a corner.
Former Portsmouth man Bance was convinced he had headed Burkina Faso level after the break, but replays showed Fatau Dauda did enough to stop the ball crossing the line.
Gyan – isolated for much of the night – nearly doubled Ghana’s lead, but he saw his first-time effort from 15 yards out cannon back off the post.
And Bance made him pay on the hour when he exploited a huge gap in Ghana’s defence to wrong-foot Dauda to deservedly draw the Stallions level.
Gyan missed a glorious chance to restore Ghana’s lead on 75 minutes, but his header flew inches wide, while Koulibaly was lucky not to have been sent off after he appeared to kick Gyan off-the-ball.
Burkina Faso thought they had struck thwe winning blow in extra-time, but Tunisian ref Sluim Jedidi ruled that Préjuce Nacoulma had fouled Kwadwo Asamoah before toeing the ball into the net.
Bance was fighting a personal battle against Ghana – Harrison Afful was the latest to clear his effort off-the-line in the second period of extra time.
Pitroipa was then sent off in the dying minutes as Jedidi showed him a second yellow card for diving, leaving Burkina Faso with ten men.
Burkina Faso will face the Super Eagles in their first-ever Afcon final, but will be without star man Pitroipa.
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