Luis Suarez grabbed his second goal of the tournament to open Uruguay's account with a free-kick after 10 minutes when he struck a low free-kick into the bottom corner that should have been easy pickings for Russian Federation keeper Igor Akinfeev.
Sbornaya suffered another setback in the 36th minute with the dismissal of Smolnikov for a second yellow card.
Uruguay have to win the match in order to finish top of the group, while a draw would see Russian Federation finish in first due to their superior goal difference.
Moments later, Russia's Igor Smolnikov was booked for fouling Vecino. Diego Laxalt's left-footed shot, following a cleared corner, looked to be heading well wide but took a cruel clip off Cheryshev, completely changing its direction and giving Akinfeev no chance.
The host nation put five goals past Saudi Arabia in the opening match of the tournament before beating Mohamed Salah and co 3-1 to put themselves top of Group A.
However, Uruguay nearly extended its lead in the 80th minute when Cavani and Suarez raced forward with only one defender to deal with.
But Cavani had the final word, prodding home in the last minute after a Godin header had been parried. Both through to the Round of 16, there was no need for either team to exert itself overly on a hot, sticky evening.
Meanwhile, the Uruguayan machine, so well oiled by Oscar Tabarez even after making four changes to the team that beat the Saudis, delivered a lesson in efficient attacking football, with battling Rodrigo Betancur orchestrating their fluid game.
Alan Dzagoev is still sidelined after picking up a hamstring injury against Saudi Arabia, although his replacement Denis Cheryshev has scored three goals in two matches.
Cavani, Suarez's strike partner, sealed the victory to open his World Cup account with a goal from close range after a corner in the 90th minute. "I hope that it continues like this for us as a team". He made quite the impression coming off the bench in the last match against Saudi Arabia and in keeping his place for this game Torreira backed up that performance with another impressive display.
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