Things went from bad to worse for the tournament hosts when they were reduced to 10 men when Igor Smolnikov picked up his second yellow card after 36 minutes.
There was plenty of noise from the stands - so Uruguay goalkeeper Fernando Muslera will have had many quieter games in terms of volume - but he had little work to do as he became his country's all-time leading appearance maker at the World Cup. It immediately looked perfectly positioned for Suarez to find the corner and he duly obliged, sweeping a crisp, low finish to Igor Akinfeev's left and putting Uruguay in the driving seat.
Goalkeeper Fernando Muslera will win his 100th cap for Uruguay after being selected to face Russian Federation in Group A on Monday.
There is a sense that Uruguay have done the bare minimum needed to top Group A, but the signs are that they are picking up form.
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.
Cavani then got on the score-sheet himself in the 90th minute as Uruguay romped to a comprehensive win.
Saudi Arabia finished third in the group standings, scoring their only goals of the tournament and vastly improving from the 5-0 thrashing by hosts Russian Federation in their opening game.
Uruguay have finished as first round group winners for just the fifth time, having done so previously in 1930, 1950, 1954 and most recently in 2010.
Yet while Smolnikov's sending off may have ended Russia's hopes of a third win, in truth the encounter had already swung decisively against them.
However, the hosts' plight took a further turn for the worse with 23 minutes played when, after Lucas Torreira's corner had been only half-cleared, Laxalt's fierce driver took a wicked deflection off Cheryshev and flew past the keeper to make it 2-0.
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. He boasted the best pass completion of any Uruguay player and also made the joint-most interceptions (3), to help his team control the game for long spells.