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.
"It's not just in this World Cup that they have not been conceding goals".
These two countries with a combined population of 13.5 million have always been overachievers on the global scene - the last decade under Tabarez has seen two-time former winners Uruguay reach one World Cup semi-final and win one Copa America, while Portugal triumphed at Euro 2016.
Cristiano Ronaldo struck four goals to spearhead Portugal through the group stages, though the Euro 2016 champions were very almost dumped out of the tournament by Iran.
That was the first goal the twice World Cup champions had conceded in the tournament in Russian Federation, but it took Cavani only seven minutes to put them back ahead at the packed Fisht Stadium overlooking the Black Sea.
Messi's return in Russian Federation was more meagre - at times he looked disillusioned on the field as Argentine struggled to find anything like their usual style and he drifted deep into midfield in the forlorn hope of influencing games. Meanwhile, three of Portugal's last four goals have come from outside the box.
Martin Caceres and Nahitan Nandez combined to create a chance but the move ended when Cavani was unable to control an awkwardly-bouncing ball, and with five minutes remaining until the break Joao Mario made a promising run down the left only to slip.
Edinson Cavani celebrates after scoring for Uruguay against Portugal. KEYS TO THE GAME Stopping Ronaldo.
And as he limped off the pitch, he was given a helping hand courtesy of Portugal's captain. The Uruguayans had gone 598 minutes since November 2017 without allowing a goal.
Then, after Pepe had drawn Portugal level from a corner kick, Cavani turned on the magic once more.