Trailing 0-1, Slimani's header in the 60th minute ensured that Algeria put their disappointment of three failed attempts -- 1982, 1986 and 2010 -- to qualify for the knockouts of the World Cup behind them and create history.
Russian forward Aleksandr Kokorin gave his team the lead with a thumping header in the sixth minute and Algerian goalkeeper Adi Mbolhi could do little to stop the 'Brazuca' whizz past him in the right corner.
The game though kept swinging from one side of the goal to another as the first half didn't see much action as far as goals were concerned.
Come the second half and Russia once again tried to double the lead through Aleksandr Samedov, but the Algeria keeper thwarted the midfielders' effort.
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Soon hell broke loose in the Algerian camp when Slimani, who has three World Cup goals to his credit so far, headed the equaliser much to the joy coach Vahid Halihodzic.
In Sao Paulo, group toppers Belgium cannot be accused of 0-0 a scoreline till half-time against a gritty South Korea as the stadium surface hindered the smooth run of play for either side.
Belgium though controlled the pace of the game in the first half and the Taeguk Warriors were only able to break forward on the counter.
But just when the jeers from the impatient crowd were getting louder the referee showed Belgium midfielder Steven Defour the red card to bring some drama to the game.
Coming onto the field with 10 players, a brave Belgium was gifted the winner by skipper Jan Vertonghen in the 78th minute.