Portugal captain Cristiano Ronaldo cut a frustrated figure during the entire match and could not add to his four goals in the first two matches, failing to improve his record of failing to score in all six World Cup knockout matches he has played.
Cavani scored twice and Ronaldo none Saturday to give Uruguay a 2-1 victory over Portugal. But the Real Madrid superstar has been at the heart of much of what went right for Portugal at this World Cup.
Portugal's Cristiano Ronaldo (L) and Uruguay's Luis Suarez challenge for the ball during the round of 16 match between Uruguay and Portugal at the 2018 soccer World Cup at the Fisht Stadium in Sochi, Russia on Jun 30, 2018.
Portugal would have to wait for the second half to equalise - with a goal in the 55th minute from Pepe.
On the same day Lionel Messi was sent home in Argentina's loss, the other "GOAT" at this tournament was also eliminated.
But Cavani secured Uruguay's place in the last eight - and a trip to Nizhny Novgorod to face France on Friday - when he steered a brilliant shot beyond goalkeeper Rui Patricio. "There is a tournament in September, the UEFA (Nations League) and we hope he will be with us to help the younger ones to grow", he told reporters.
'We must congratulate Uruguay because they are the national team that are in the quarter-finals, ' Ronaldo said after the game.
Back came Portugal but, after a good spell of pressure, Joao Mario's cross was too deep for Ronaldo and Muslera claimed.
'Up to this game people were saying that we might have won the group but the group was not easy, ' said Tabarez.
Bernardo Silva drove in a low cross that deflected over as Portugal began to run out of time, and then Nandez was replaced by Carlos Sanchez for Uruguay.
The spirit with which they play, sticking into tackles, putting their bodies on the line to get to the ball and working hard for their teammates sets them apart from nearly all other teams in the draw, and gives them an added edge besides just the football playing.
Cavani was forced off in his team's last-16 match against Portugal in the second half with a leg injury, in what is a worrying sign for the Uruguayans.