Uruguay, on the other hand, are threatening on the counter.
The only downside for Oscar Tabarez's side was the sight of Cavani limping off late on, raising a question mark over his fitness for next week's last eight showdown with the French in Nizhny Novgorod.
"Now is not the time to talk about the future of players and coaches", Ronaldo said.
Either side of Suarez's chance, it was all Portugal - from possession, to meaningful possession and scoring chances - and finally, after trailing for almost 50 minutes, they were level after 55 minutes, thanks to Pepe's unmarked header from Raphael Guerreiro's corner kick.
"The truth is, it was really exciting", Cavani said.
"It's exciting. there are no words to describe this".
However, Cavani struck a well-placed shot in the 62nd minute to ensure that Portugal moves on to the quarter finals.
Guerreiro fired over from the edge of the box after a corner had fallen to him, and then Ronaldo laid the ball back to Adrien Silva, whose shot was deflected behind for a 55th-minute corner.
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Game kicks off at 6pm GMT.
This was Portuguese star Cristiano Ronaldo's 38th game in World Cups/European Championships - no player has played in more across the two competitions (equal with Bastian Schweinsteiger).
Earlier in the day, France beat Argentina 4-3 and sent Lionel Messi and his squad packing.
It took Uruguay just 7 minutes to get on the scoresheet and it was the strike duo of Luis Suarez and Edinson Cavani working their magic to give the South American side the lead. Ronaldo ran in front of Pepe and drew the attention of both Gimenez and Godin.
However, 10 minutes later, Cavani was done, limping off in obvious pain.
EARLY GOAL It was a five-pass build-up from deep in its own end that culminated in Uruguay's first goal, and the final two passes were flawless.
His first goal on Saturday involved an incredible, cross-field combination with Luis Suarez. Suarez makes a brilliant cross from the left for Cavani to head the ball past the goalkeeper.
However, Uruguay soon led again when Cavani curled in a peach of a finish, though his delight soon turned to anguish as the striker limped off after appearing to pull a muscle.
Ronaldo had company everywhere he went on the field and Portugal's supporting cast was unable to provide enough help.
"I hope it's going to be a great clash between these two teams because it's very different from the group stages - either you win or you lose".