In a fast start, Uruguay were ahead inside 10 minutes as Suarez, who scored the victor against Saudi Arabia on matchday two, found the net with a pinpoint free-kick.
Luiz Suarez broke the deadlock in the 10th minute through a spectacular freekick, They doubled their lead through an own goal from Cheryshev in 23th minute.
Oscar Tabarez's charges were dominating the encounter, while Russian Federation were all over the place at the back as they failed to recover from a poor start.
That silenced a vociferous home crowd which had been in party mode after Russia's opening two victories and were not expecting their final group contest to be effectively ended in the 36th minute when Igor Smolnikov was sent off.
A resultant corner from one such strike brought the third goal as Cavani was close at hand to nod in after the goalkeeper had done well to keep out a glancing header from Godin.
The Russians, who were playing with 10 men for nearly an hour, had no chance against the first strong team they had encountered in the tournament, after their early wins had created the impression they could go far.
Cavani sealed the win on 90 minutes by tapping home the rebound, after Akinfeev had parried Godin's header.
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For Uruguay's demanding coach Oscar Tabarez, whose side had not hit top gear in their previous two matches, it was a case of job done - even if there was certainly no cause for celebration. We wanted to play in the same way we did before.
Uruguay, controlling possession and playing the ball around confidently, exposed the hosts for what they are - the lowest-ranked team in this World Cup.
On a personal level I'm happy to move forwards, with the team we continue to make history.
In the other match of this group of Saudi Arabia for the first time since 1994 won the world Cup.
They had spluttered in defeating Egypt and Saudi Arabia 1-0 but came out of the traps quickly vs. Russian Federation. The 2016 European champions will next face Uruguay on Saturday in the round of 16.
Seeing as the Russians' next match will be against Group B winners Spain in the round of 16 on Sunday, it's hard to disagree with their manager's assessment.
When Russia take on Spain on Sunday, Cherchesov will find out just how useful it was.
Quaresma's goal came on a night when Ronaldo - who had scored all four Portugal goals in its first two games - was denied on a penalty shot.