Suarez went close to a second when Patricio pushed out his 22nd-minute free-kick and Cavani shot wide in the final moments of the first half after controlling Godin's towering punt.
Uruguay's win means Portugal were eliminated once again in the knockout round.
On the same day, Ronaldo and Lionel Messi exited the World Cup without having ever scored in the second round of the competition.
Uruguay chased every ball as if it was their last, with Cavani often dropping back to form a five-man midfield.More news: Trump Says He Will Announce Supreme Court Pick On July 9
Uruguay are hopeful Jose Maria Gimenez will return from injury to resume his centre-back partnership with Atletico Madrid team-mate Diego Godin. Suarez held up play for a few seconds to give Cavani time to arrive at the goal, then cut back and laced a ideal cross that ricocheted off Cavani's face and into the back of the net.
It was a five-pass buildup from deep in their own end that culminated in Uruguay's first goal, and the final two passes were ideal.
Ronaldo then walked over, helped pick Cavani up and aided him off of the field.
Instead, Tabarez knows that the best way to nullify Ronaldo and heighten Uruguay's chances of reaching a World Cup semi-final, his side "will have to work collectively in order to try to limit the effect that he can have". He didn't manage to touch the ball a single time in Uruguay's box in the first half, such was its defensive tenacity.
"When it comes to the rivalry with Ronaldo at club level that's a different thing altogether", he told reporters ahead of Saturday evening's clash at the Fisht Olympic Stadium. Cavani continued his run and Suarez curled the pass to the back post while Portugal defender Raphael Guerreiro was watching. KEYS TO THE GAME Stopping Ronaldo. "He is the best player in the world in my opinion and it's natural that the team depends on him, but you can ask the same question to Uruguay's coach too, if his team depends on Suarez or (Edinson) Cavani ..."