The Uruguayan player, acquired from Benfica for an initial fee of €75 million, made himself an instant fan favourite after capping a lively appearance off the bench with a stoppage time goal to secure the first trophy of the season.
Despite being without Nunez in the first half, Liverpool were quick to strike, with Trent Alexander-Arnold opening the scoring in the 21st minute. His first-time strike took a slight deflection off the head of Nathan Ake and nestled in off the post.
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City's Erling Haaland started his second game since signing for Pep Guardiola's team and spurned two chances to draw level shortly before half-time.
Jurgen Klopp introduced new man Nunez from the bench an hour in, and Liverpool continued to look dangerous going forward, with City desperate for an equaliser.
And while all eyes were on Haaland, it was another summer signing -- Julian Alvarez -- who drew the game level in the 70th minute.
The Argentina forward squeezed a shot past Adrian after a goalmouth scramble that saw Phil Foden win the ball from the Spanish goalkeeper. Alvarez's goal was initially ruled out as his original run in behind was deemed offside, but a lengthy VAR check ended with Craig Pawson overturning the decision.
But the goal didn't keep City on level terms for long. Nunez drew a handball from Ruben Dias in the penalty area that eventually was awarded through VAR as a penalty. Mohamed Salah dispatched the spot kick with ease.
Victory was ensured for Klopp's side in added time -- and Nunez got his goal. He nodded home past Ederson to give Liverpool a two-goal cushion and ensure a perfect start to his tenure at Anfield.
"Our season started today, and it was important for us to get off on the right foot," said Alexander-Arnold, who was full of praise for 23-year-old Nunez's impact.
"He won the penalty, scored a goal and looked very lively. He's been brought in to score goals, and he's proved he can do that today," he said.
"He's a top player, a young player who is willing to learn. He's bonded well with the lads. He came on with a point to prove".
Information from Reuters was used in this report.