Denis Cheryshev then had the misfortune to double Uruguay's lead in the 23rd minute, a shot from Diego Laxalt that was going wide clipping his heels.
Matters were made worse for Russian Federation in the 36th minute, Smolnikov picking up his second booking after lunging in on Cavani, just eight minutes after being carded for a foul on Matias Vecino.
The atmosphere in Samara was loud and festive but Suarez found the ideal way to dampen it within 11 minutes. Uruguay registered 17 shots to Russia's three. It was nearly three soon after when fine work from Suarez set up Rodrigo Bentancur, whose effort was saved.
Things then got worse for Russian Federation when Smolnikov, already on a yellow card, was sent off after taking down Laxalt. In-form winger Cheryshev was substituted as a result with manager Stanislav Cherchesov seeking to shore things up.
But Cavani had the final word, prodding home in the last minute after a Godin header had been parried.
Russia's impressive start to the World Cup took a downward turn as they had a man sent off and were easily defeated by Uruguay, whose victory means they top Group A. "When they feel comfortable or at home, they score goals".
La afición de Irán despierta en plena noche a Cristiano Ronaldo
Históricamente el tercer partido para los iraníes significaba jugar por el honor. Ambas selecciones necesitan ganar para acceder a los octavos de final.
They will take on the Group B victor on July 1.
There is consolation that this was not their full-strength team and that, when they play in the last 16, three key players will be relatively fresh. There are many options for Tabarez to choose from, now it's up to him to select the best one.
The Association of British Travel Agents is reporting a rush on requests from England fans trying to get to Russian Federation for the World Cup.
SARANSK, Russia - Cristiano Ronaldo's missed penalty cost Portugal first place in its World Cup group.
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. Gimenez scored in the team's opening match of the tournament, a 1-0 victory over Egypt.
Birthday boy Rodrigo Bentancur, plying his trade for Italian champions Juventus, should have put the tie to bed in the 29th minute but the promising midfielder's close range effort was blocked by the legs of Igor Akinfeev.
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.