The striker, who missed the opening 2-1 defeat by Senegal due to a mild bout of malaria, drilled home a long upfield punt just as a tepid clash between the continent's two heavyweights seemed to be heading for a stalemate.
The result left Ghana, Algeria and Senegal on three points in Group C with the latter playing South Africa (zero) in the evening kickoff (1900 GMT).
Littered with errors and fouls in the first half, the game came to life after the break but produced no clear-cut chances until the talismanic Gyan struck to ease the pressure on Ghana coach Avram Grant, the former Chelsea boss.
Gyan showed his class when he took the ball in his stride and, with a defender closing him down, produced a bobbling shot from a tight angle that went past keeper Cedric Si Mohamed.
Algeria, the top-ranked team in Africa, dominated the opening 30 minutes but defender Madjid Bougherra had to glance away a teasing cross from the right to deny Gyan a clear header at goal.
Ghana's skipper then twice misfired woefully wide from good positions, either side of a flicked effort by Jordan Ayew which fizzed just over the bar.
With time running out and Grant frantically yelling instructions from the touchline, substitute Mubarak Wakaso belted a hopeful ball up field and Gyan produced a moment of magic to delight his team mates.
LOT OF EMOTION
"This is a game with a lot of emotion," said a delighted Grant. "I didn't like it when we conceded a goal in the last minute (against Senegal) but this time we scored in the last minute.
"We deserved it, we were the better team. Asamoah has a fantastic attitude and he proved his ability in an important game but I have to praise the whole team because they worked very well as a unit in both good and bad moments."
Algeria's French coach Christian Gourcuff, who took charge despite the death of his mother on Thursday, rued his team's costly lapse in concentration.
"It’s cruel to lose a game in the last minute and it fundamentally changes the group," he said.
"A draw would have put us closer to the next round and we deserved that. The pitch and the weather were also a factor. We now have to go all out in the next game against Senegal."
(Writing by Zoran Milosavljevic, additional reporting by Mark Gleeson, editing by Tony Jimenez)
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