Luis Suárez gave Uruguay the lead after 10 minutes with a superb free-kick just outside the penalty area, taking advantage of a gap created by Sergei Ignashevich tussling with Edinson Cavani.
Russian Denis Cheryshev then had the misfortune to double Uruguay’s lead in the 23rd minute, a shot from Diego Laxalt that was going wide clipping his heels.
The hosts’ hopes were then finished off by Igor Smolnikov picking up two yellow cards in rapid succession.
Uruguay sealed the deal in their favour in the 90th minute when Cavani followed up a header from Diego Godín that was saved by Akinfeev after a late corner, only for Cavani to tuck away the rebound.
Uruguay will next play the runners-up of Group B in the last 16 on Saturday in Sochi.
Russia, meanwhile, have finished second and will play the winners of Group B in the last 16 on Sunday at the Luzhniki Stadium in Moscow.