Gervinho, Siaka Chico Tiene and Didier Drogba were on target as tournament favourites Ivory Coast survived Emmanuel Eboue's sending off to secure their first victory of the African Nations Cup.
It was 1-0 to Ivory Coast on 55 minutes when Arsenal midfielder Eboue received a straight red card for a reckless two-footed tackle.
Matthew Amoah struck a post as Ghana came close to an equaliser, but Tiene smashed in a stunning free-kick after 66 minutes, and Chelsea striker Drogba headed in a 90th-minute third.
Asamoah Gyan converted a penalty with the last kick of the game, but it was nowhere near enough to prevent the Elephants from progressing to the quarter-finals.
Earlier, Gervinho had finished off a fluid counter-attacking move after 23 minutes.
With Togo withdrawing from Group B, Ghana have to beat Burkina Faso on Tuesday to join Ivory Coast in the last eight.
The Black Stars, though, looked lethargic throughout in their first game of the tournament, even after Chelsea midfielder Michael Essien -- on his way back from injury -- came off the bench at half-time.
Ghana will have to improve significantly if they are to defeat Burkina, who tenaciously held Ivory Coast to a draw in their first match.