Suarez slotted a 20-yard free kick into the bottom corner, after defender Sergei Ignashevich had made the target bigger for him by abandoning his position at the end of the wall.
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. Aleksei Miranchuk replaces Aleksandr Golovin whilst Igor Smolnikov and Fyodor Kudryashov come in as full backs.
The hosts' hopes were then finished off by Igor Smolnikov picking up two yellow cards in rapid succession. The full-back, already on a booking for a foul on Cavani, recklessly took down the rampaging Laxalt on the left wing to become the third player sent off at this World Cup.
Cavani finally got his goal in the 90th minute with a simple finish from close range after Akinfeev had saved Diego Godin's header, 3-0.
This is the first time Uruguay have won all three group games at a World Cup finals.
Uruguay stamped their authority early in the group decider.
It was Suarez's second goal of the tournament and seventh World Cup goal overall for Uruguay, with only Oscar Miguez having scored more for the South Americans with eight. He will also break his nation's record for World Cup appearances, with 14.
In truth, there was not an outstanding performer on either side in a game which had a testimonial feel to it in the second half, but Lucas Torreira was effective in midfield for the winning side.
Dzyuba did have one opportunity to set up an exciting finish on 74 minutes when Russian Federation pinched possession in the final third, but the 6ft 5in striker could not bend his shot inside the post after checking back onto his left foot. His corner also led to the Cheryshev own goal which ultimately secured top spot in the group.