"Statistics are there to be broken", Suarez said. Both through to the Round of 16, there was no need for either team to exert itself overly on a hot, sticky evening.
Edinson Cavani also scored Monday against the host nation, which dropped its first match of the tournament. Both teams are already assured of spots in the round of 16, but they will be fighting to top Group G.
"I believe that when we had 10 people in the pitch, we were running and wanted to attack more", said Russian Federation coach Stanislav Cherchesov.
While Russia had confounded those who predicted a group stage exit with resounding victories over Saudi Arabia and Egypt, there was still a question mark over how they would perform when they faced stronger opposition.
But Uruguay - ranked No. 14 in the world - posed a far greater challenge to the hosts.
There was a party atmosphere around the scorching Samara Arena before kick-off, with fans having travelled from all over the country keen to share in the good feeling surrounding their national team.
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. In 2010, he used his hands to block Dominic Adiyiah's header and then celebrated when Ghana missed the penalty kick.
Current Group B leaders Spain play Morocco, who are already eliminated.
Luis Suarez opened the scoring in the 10th minute with a low free-kick and Denis Cheryshev deflected a Diego Laxalt shot into his own net (23) before Igor Smolnikov was sent off for a second yellow card nine minutes before half-time.
Cavani scored in the 90th minute and was taken out a short time later.
But Cavani had the final word, prodding home in the last minute after a Godin header had been parried.
Uruguay made four changes as Nahitan Nandez, Lucas Torreira, Diego Laxalt and Sebastian Coates came in, replacing Jose Gimenez, Guillermo Varela, Cristian Rodriguez and Carlos Sanchez.
"We have reached our goal to be first in the group", Suarez said in first television interviews.
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. "As for our team, we will do our best to fulfill our own potential and to overcome our own problems as we must not fail repeating the mistakes of the past".