Algeria placed second in Group H behind Belgium with four points, meaning it will meet Germany in the Round of 16.
The victory prompted mass celebrations on the pitch among the players, and had coach Vahid Halilhodzic shaking his head with disbelief.
Russia, needing a win to advance, went on the attack from the start and dominated the first half with its intricate and swift passing movements through midfield. The Russians took the lead as early as the 6th minute when Alexander Kokorin powerfully headed in a left-foot cross from Dmitry Kombarov.
However, there were indications on the TV broadcast that a green laser was being shone toward the goalkeeper's face just before the free kick was taken.
Also Read
Brahimi had troubled the Russia defense consistently until his substitution late in the game. Along with midfielder Sofiane Feghouli, he helped neutralize much of Russia's attacking intent through the second half.
Before Algeria's equalizer, Russia had chances to double its lead, notably in the 26th minute when Oleg Shatov weaved through the Algeria midfield but his right-foot shot drifted wide of the Algeria post.
Algeria came closest to qualifying for the second stage at the World Cup in 1982, but West Germany and Austria played out a result that suited both of those teams. The European teams, meeting a day after Algeria had won its last group game, knew that a 1-0 win for West Germany would put both through to the second round at Algeria's expense. It remains one of the most contentious group games in the tournament's history.