Standing in their way in the second round will be Germany, who confirmed their spot as Group G winners earlier today.
Below, Sports Mole assesses whether Algeria did enough to earn a point against their group rivals.
On target: 6
On target: 4
Was the result fair?
With plenty riding on the result of this fixture, the contest was competitively fought throughout the 90 minutes and a draw was probably a fair result. It was a point that was worth nothing to Russia, but they didn't do what was required to claim that they deserved a place in the last 16 more than their opponents.
Algeria's performance wasn't easy on the eye in the opening stages but after keeping Russia's advantage down to a solitary goal, it gave them the confidence to throw caution to the wind in search of an equaliser. They didn't test Igor Akinfeev on too many occasions, but when they did, they took advantage of the indecision shown by the stopper to get back on level terms. After that goal, they were rarely tested by the hosts of the next World Cup finals and they will be delighted to reach the second round.
Fabio Capello's team got off to the perfect start when Kokorin powered a header into the top corner, but they were unable to capitalise on that goal and barely brought a save out of Raïs M'Bolhi. Aleksandr Kerzhakov was their main threat, but as his influence faded Algeria grew in confidence and the European side had nothing left in reserve to force a late winner.
Sports Mole's man of the match
Yacine Brahimi: Yacine Brahimi may have only played eight games for his country but he delivered a display that a World Cup veteran would have been proud of. Like his team, it took a while for the Granada winger to grow into the game, but when he did, he frequently terrorised the Russian defence with his pace and the 24-year-old can be pleased with his night's work.
Russia goalkeeper Akinfeev was at fault in his team's opening game against South Korea, and it was a similar story tonight. The CSKA Moscow stopper attempted to come for a ball that he was never going to get and it left Slimani with the simple task of heading into an empty net. If it wasn't for the 28-year-old, Russia may have qualified for the second round.
Overall, Cuneyt Cakir didn't produce a bad showing in Curitiba, but his lack of consistency with his cards would have irked both coaches. A couple of players were harshly cautioned whereas a number of tougher challenges went without any punishment. However, Cakir didn't affect the result of the match, so he can class his display in the above-average bracket.
Algeria: After their famous win this evening, Algeria will move in to play Germany on Tuesday for a place in the quarter-finals.
Russia: Russia will return home in the next 24 hours contemplating which direction they will now go in after a disappointing tournament that has seen them fail to register a win.