Dempsey tapped into the net from close range in the 21st minute after being fed by Herculez Gomez, who had just had a shot parried by Algeria goalkeeper Rais Bolhi in a goalmouth scramble.

Rafik Djebbour came closest to scoring Algeria's first goal of the tournament, hitting the crossbar in the 6th after US defender Jay DeMerit failed to clear a long ball.

Algeria needs to win to have any chance of advancing from the group while a draw could be enough for the United States depending on the result in the other Group C match between England and Slovenia.