The Al Ain striker missed Ghana's opening Group C defeat to Senegal with a bout of malaria but was the hero for Avram Grant's side as his composed finish in stoppage time earned a crucial three points.
The first half proved a lacklustre affair with chances at a premium, although Nabil Bentaleb will feel he should have put Algeria - the highest ranked team in the tournament - into a first-half lead when he skewed wide from close range.
Ghana improved after the break, though, and Gyan flashed a header wide before Andre Ayew nodded over the crossbar when free in the penalty area.
The Black Stars were rewarded for their improved showing with Gyan's late strike, and a win for Ghana leaves them and Algeria on three points, while Senegal can move to the brink of the last eight by beating South Africa in Group C's other clash later on Friday.
