Ghana, appearing in the play-off for only the second time, took a 10th-minute lead thanks to a powerful left-foot free-kick from Portsmouth midfielder Sully Muntari which flew through the hands of keeper Tiasse Kone, the only local in the Ivorian squad.
Sanogo, who plays for German Bundesliga club Werder Bremen, equalised after 24 minutes by sprinting on to a through ball, holding off giant defender John Mensah, and placing the ball wide of goalkeeper Richard Kingson.
Eric Addo had a close-range header well saved by Kone, while Kingson denied Kalou and captain Didier Drogba before Ivory Coast took the lead on 32 minutes at the Baba Yara Stadium.
Black Stars rise late
Kingson blocked a close-range Drogba effort, but the rebound rolled kindly for Sanogo, whose tap trickled over the line to complete first half scoring.
A tame second half came to life after 70 minutes when substitute Owusu-Abeyie left several Ivorians trailing as he turned on the pace before firing under Kone to restore parity in the clash of west African giants.
Agogo scored his third goal of the Nations Cup on 80 mintues to edge the Black Stars ahead, springing an offside trap to burst through and give Kone no chance.
There was no stopping Ghana in the closing stages and Draman added a fourth five minutes from full-time with a shot from outside the penalty area that took a sudden bounce leaving Kone embarrassed as the ball flew over him.
Egypt and Cameroon will contest the final in Accra on Sunday.