Russia, the lowest ranked team in the field at No. 70, went down to 10 men after right back Igor Smolnikov received a second yellow card in the 36th minute.
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.
With both teams already qualified for the last 16, Russian Federation coach Stanislav Cherchesov also made three changes to the side that beat Egypt 3-1.
The team of Stanislav Cherchesov has tried to answer their sharpness in the attack, but Alexander Samedov, who had the most critical moment, missed your chance.
The hosts were rewarded with their best chances of the match, the first to Artem Dzuba, who fired wildly over the bar from inside the box, the second by Fedor Smelov, who dazzled to find space in behind the Uruguay defence but failed to pick out a team-mate with what looked to be an easy cut-back.
Meanwhile, Saudi Arabia managed their first win in Russian Federation after beating Egypt 2-1 with a last-gasp victor that eclipsed Egyptian talisman Mohamed Salah's 22nd minute goal.
In the second round, Uruguay will meet Group B runners-up Portugal, who toiled to a 1-1 draw with Iran to allow Spain to steal in and take first place. The Paris Saint-Germain forward put a rebound into the left corner of the net after Diego Godin's header was parried by Akinfeev. We wanted to win; we did not watch where we were playing. Egyptian keeper Essam El-Hadary became the oldest player ever to appear at a World Cup at 45-years-old. Egypt at the 2018 world Cup lost all three matches.
Salem Aldawsari scored with nearly the last kick, shooting from a tight angle inside the Egypt penalty area and poking the ball past El Hadary.
Hosts Russia and their expectant fans were given a brutal reality check on Monday when Uruguay exposed the weaknesses in the side that had been papered over in the uplifting victories over Egypt and Saudi Arabia in World Cup Group A. The decision was confirmed after a video review.
Russian Federation is holding its first time ever edition of the FIFA World Cup, which kicked off in Moscow with a spectacular opening show at the Luzhniki Stadium on the night of June 14.
Uruguay have finished as first round group winners for the fifth time, having done so previously in 1930, 1950, 1954 and 2010.