Slimani scored the opening goal in the 26th minute. He plays for Portuguese Primeira Liga side Sporting Clube de Portugal.
Algeria won 4-2 over South Korea, following a 3-0 half-time lead at Estadio Beira-Rio in Porto Alegre, southeastern Brazil.
South Korea, which had a 1-1 draw against Russia in their Group H opener, is on the verge of elimination from the Round of 16.
South Korea will face Belgium on Thursday in Sao Paulo.
Belgium won 1-0 over Russia in another Group H match earlier Sunday, and is qualified for the 16-team knockout stage.
Followings are the Group H standings after Sunday's matches at the 2014 FIFA World Cup in Brazil.
Teams W D L Points
Belgium 2 0 0 6
Algeria 1 0 1 3
Russia 0 1 1 1
S. Korea 0 1 1 1