Uruguay looked the likelier side in the first half before Liverpool forward Suarez broke the deadlock on 48 minutes when he skipped beyond a couple of home shirts from Diego Perez's pass before sending a shot spinning past Russia goalkeeper Viacheslav Malafeev.
The South Americans were still celebrating their lead when Russia pegged them back a minute later courtesy of a fine finish by substitute Alexander Kerzhakov - who replaced the toiling Fulham forward Pavel Pogrebnyak at half-time - as he lifted the ball over Nestor Muslera with the visiting defence cut wide open after Diego Godin had blocked his initial attempt.
Russia introduced a number of squad players in the second half. They open their Euro 2012 campaign against Group A rivals Czech Republic on June 8 in Wroclaw. They will fancy their chances of qualifying from the weakest group at the finals with Greece and Poland their other opponents.
"I think we could have won, I missed a couple of chances," said Kerzhakov. "The thing I liked the most is that we didn't give way to the South American champions. We played very well today. I think we can still improve."
Russia were without defender Roman Shishkin, who was sent home from training after losing weight during a bout of gastritis.
Outgoing coach Advocaat – who joins PSV after the finals – was also without stopper Vasily Berezutsky, who was ruled out earlier this week after failing to recover from a hip injury.
This means Advocaat now only needs to drop one player from his 24-man squad for the finals. Lokomotiv Moscow midfielder Magomed Ozdoyev is expected to be the man who misses out.
Uruguay - building towards the South American World Cup qualifiers - certainly looked the slicker side in the first half with Suarez, Edison Cavani and Diego Forlan proving to be a potent blend.
Suarez hammered a shot wide of goal on 17 minutes when he should have netted with Cavani lifting an effort over the bar four minutes later.
Kherhakov had the ball in the net for Russia with the score at 1-1, but the goal was disallowed for offside with Muslera forced to dash off his line to save at the feet of Kerzhakov as it became clear there would be no further scoring amid the rash of substitutes.