Javier Mascherano brought him down and Griezmann crashed the subsequent free kick off the bar from 25 metres but France only had to wait a couple of minutes to break the deadlock.
"I think there is often a mistaken assumption that possession leads to scoring opportunities", Uruguay's long-serving coach Oscar Tabarez told reporters.
EDISON Cavani upstaged Cristiano Ronaldo, first with his head and then with his right foot, and sent Uruguay to the World Cup quarterfinals.
Uruguay took the lead through Edinson Cavani before Portugal responded in the second half with a header by Pepe. Diego Simeone has enjoyed great success at club level, so why can't Uruguay, with not just one but two outstanding strikers?More news: Serbia 0 - 2 Brazil - Match Report & Highlights
Against Uruguay, though, we saw the reality of Portugal's overreliance on the Real Madrid forward.
34 minute: Portugal are pressing hard to equalise but fail to hold the ball in the final third.
And after Portugal equalised with Pepe's header in the 55th minute, it was Cavani again finishing a ideal Uruguay counter in the 62nd with a shot from just inside the penalty area that caught Portugal goalkeeper Rui Patricio slightly out of position and curled inside the far post.
Uruguay won all three of their group matches, beating hosts Russian Federation 3-0 in their last outing, and are the only team yet to concede a goal at the tournament.
Portugal coach Fernando Santos is adamant his captain will continue to make himself available for selection and when asked if Ronaldo still will be in action at the European Championships in 2020 and the World Cup two years later, he said: 'Certainly, yes.More news: Pete Davidson confirms engagement to Ariana Grande
In the final moments of the half, with Suarez down following a challenge from Raphael Guerreiro, Portugal won a corner that came to nothing before a half-chance was steered wide by Cavani at the far post.
Where is the FIFA World Cup 2018 Uruguay v/s Portugal match?
And just like that, he joined Messi in heading out of Russian Federation and out of the World Cup.
Since the format of the World Cup changed in 1986 to include a round of 16, Uruguay have been eliminated on three of the four occasions they have reached that stage, losing in 1986, 1990 and 2014, but progressing in 2010 against South Korea.
Quaresma bent a cross towards Ronaldo, but just over him, and Bernardo Silva's low ball in was cleared before Manuel Fernandes came on for Portugal in place of Joao Mario. Godin, 32, is one of the most senior players in the Uruguay squad, making his debut in 2005 and playing at three World Cups as well as winning the Copa America in 2011.More news: Prince William arrives in Israel as part of regional tour
Remarkably, the pair pack their bags still never having scored in a World Cup knockout game.
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