The recent Manchester City signing was quiet during the group stage in Equatorial Guinea but came to life to help the Elephants to victory in this quarter-final showdown.
He got his first goal of the competition on 26 minutes to put the Ivorians in front and then headed in the crucial second goal midway through the second half after Hilal Soudani had equalised for Algeria.
Herve Renard's side will now take on DR Congo in the semi-finals in Bata on Wednesday as they chase their first continental title since 1992, with the winner of that facing either Equatorial Guinea or Ghana in the final itself.
Meanwhile, Algeria go home having ultimately failed to live up to their billing as pre-tournament favourites.
Renard made just one change from the side that beat Cameroon in midweek to qualify for the knockout stage, with Seydou
Doumbia making way for Gervinho, who was available again after a two-game ban.
Algeria coach Christian Gourcuff went with the same team as that which beat Senegal 2-0 in their last group game, and it was the
Desert Warriors who started the brighter at the Estadio de Malabo, with Soudani forcing an early save from Sylvain Gbohouo in the Ivorian goal.
However, the Ivory Coast front three started to come to life after Max-Alain Gradel moved across to the right flank, switching sides with Gervinho.
The little Saint-Etienne winger cut inside before firing a shot just wide to signal the Elephants' emergence as an attacking threat.
Midway through the first half they came closer still, Serge Aurier leaping at the back post to head a Gradel free-kick against the post with Rais M'Bolhi in the Algeria goal beaten.
And the breakthrough arrived 26 minutes in, Eric Bailly driving into the opposition half and finding Gradel, whose cross to the back post was headed in by Bony as the Algerians appealed in vain for offside.
Saphir Taider and Faouzi Ghoulam both tried their luck from range but Gourcuff's side were unable to find an equaliser before the interval.
Nevertheless, they needed only six minutes after the restart to restore parity, with the help of some questionable Ivorian defending.
Gbohouo came off his line to try to meet a long ball downfield only to hesitate, and Bailly then failed to clear a Riyad Mahrez cutback from the left, allowing Soudani an easy finish.
However, Gbohouo redeemed himself with a remarkable save to deny Soudani from point-blank range as the striker tried to help a Yacine Brahimi shot into the net.
The Ivorians took full advantage as they went back in front on 68 minutes, Bony leaping to head in a free-kick from his new Manchester City colleague Yaya Toure.
Gbohouo was called into action again four minutes from time to keep out a Ghoulam free-kick as Algeria pushed forward, but it was the Ivorians who scored again as Gervinho finished off a counter-attack in stoppage time.