Both sides made 3 changes each, and two, in particular, stood out: Torreiro in for Uruguay and Golovin out for Russian Federation.
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.
The host nation's hopes of staging a memorable comeback were dealt a near-fatal blow when Igor Smolnikov saw red after picking up a second yellow card in the 36th minute.
Uruguay, by contrast, are perfectly set-up to keep teams at arm's length and they had few problems during a second period that at times meandered to a procession, Edinson Cavani converting from close range in the final minute to complete a comfortable 3-0 victory.
Because Russia had the advantage in goal differential from its first two group matches, it would have won the group with a draw.
"We throw our hearts into the game, including our joy, and always do our utmost at a hundred-percent level", Cavani told journalists in Samara.
It was Suarez's seventh goal in three World Cups, while it was only a third for Cavani.
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Luis Suarez grabbed his second goal of the tournament to open Uruguay's account with a free kick after 10 minutes and they doubled the lead with an own goal from Russia's Denis Cheryshev soon afterwards.
A song by comedian Semyon Slepakov went viral just before the tournament, poking fun at Russia's poor form and suggesting players needed Chechnya's authoritarian leader, Ramzan Kadyrov, as coach for extra motivation.
Having replaced Cheryshev with Mario Fernandes in the immediate aftermath of Smolnikov's premature departure, Russian Federation boss Stanislav Cherchesov sent on midfielder Daler Kuziaev for Yuri Gazinsky at the break and saw his team rally. Gimenez scored in the team's opening match of the tournament, a 1-0 victory over Egypt.
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.
However, it is likely that their opponents there will be Spain - with the 2010 World Cup winners expected to secure their place as Group B winners with a victory over Morocco later this evening, although Portugal could top the group with a better result against Iran.
Uruguay are the first side to win all three of their group games without conceding a single goal since Argentina in 1998 (seven goals scored, none conceded).