Cameroon beat Senegal 5-4 on penalties after a goalless 120 minutes in Franceville, southern Gabon, in the day's second game following a 2-0 win for Burkina Faso against Tunisia in Libreville earlier.
Mane was the only player to miss from the spot in the shoot-out in Franceville, with Cameroon goalkeeper Fabrice Ondoa saving his effort from 12 yards.
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Vincent Aboubakar then stepped up to score and take the Indomitable Lions through to the last four at the expense of a Senegal side who were one of the favourites coming into the tournament.
Cameroon, who also defeated the same opposition on penalties in the final of the 2002, can now look forward to a semi-final tie against either DR Congo or Ghana in Franceville on Thursday.
It is the first time Cameroon have reached the last four since 2008, when they lost to Egypt in the final in Ghana.
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"We have the possibility to write a beautiful page in our history and we do not want to stop here," said Cameroon captain Benjamin Moukandjo. "We're going one game at a time. We have a semi-final to play, and whoever it is against we hope it will be as beautiful as this."
Senegal had enjoyed the better of the chances in normal time, but could not find a way past Ondoa, who was in inspired form. "Our performance was good. We tried to play football against a side who were well organised and got men behind the ball," said the Senegal coach Aliou Cisse. "We know about penalties. It comes down to luck. They won it and I wish them good luck."
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