The Paris Saint-Germain marksman, who now has three goals to his name this tournament, also showcased his usual selfless running and pressing before being forced off with injury.
Griezmann's strike from the spot was not as clean as his free kick but goalkeeper Franco Armani went the wrong way.
"But we will take a look at him".
Ronaldo could not add to the four goals he scored in the group stages.
Parity was to last just seven minutes, however, as Cavani soon returned to haunt the Portuguese defence with his second of the night in the 62nd minute.More news: Priyanka Chopra: Nick Jonas Is One of My Favourite Men'
His second came after 68 minutes at the end of a beautifully flowing French move with Olivier Giroud providing the subtlest of touches to lay the ball into Mbappe's path and the teenager finishing right-footed with some elan.
2 minutes of Stoppage time!
It was from another sort of dead-ball delivery that Portugal found a chink in the armour, Pepe equalising with a header from a corner after the break.
Uruguay form: Uruguay qualified from the group phase with an unblemished record and are hoping to carry that momentum into the latter stages.
Cavani put Uruguay ahead in the seventh minute when he evaded the Portugal defence to meet Luis Suarez's pinpoint cross with a bullet header at the far post. "I think all of us have come here to play and when our moment comes we will be ready for it to help Portugal win", he said. I don't have words to describe it. "There is a fantastic group with enormous ambition that wants to succeed and I am very confident that the national team will continue to be at the highest level". Portugal, ironically after their talisman limped off early due to injury in the final against France, achieved their dreams by winning Euro 2016, so this small European nation has already savoured a success it perhaps never truly imagined.
Uruguay coach Oscar Tabarez was complimentary of Ronaldo and the rest of the Portugal squad, noting several times Uruguay will be facing the reigning champions of Europe.