In a tale of two big summer signings, Nunez came off the bench to win a penalty and score his first goal since a 75-million euro (B2.8 billion) move from Benfica, while Erling Haaland had a City debut to forget.
“He’s good,” said Klopp on Nunez, who has been criticised for his pre-season performances. “Today we played the smart passes. We saw Darwin in dangerous situations. He used the spaces and finished well too.
“All the subs made a real difference. It was the most important thing I learned today, that the boys are ready.”
Trent Alexander-Arnold’s blistering strike gave Liverpool a deserved half-time lead in Leicester.
But it was City’s other new forward who hauled Pep Guardiola’s men back into the game after the break as Julian Alvarez equalised.
Tying down Mohamed Salah to a new three-year deal was Liverpool’s other major piece of summer business and the Egyptian was deadly from the penalty spot after Nunez’s header was handled by Ruben Dias.
The Uruguayan then got his own glory moment by stooping to head home in stoppage time before tearing off his shirt in celebration.
Victory saw Liverpool win the traditional season curtain-raiser for the first time since 2006 and lay down an early marker in what is expected to be another battle between the sides for the Premier League title.
City held off the Reds to win the Premier League for a fourth time in five years by a point in a thrilling finale to last season.
Guardiola’s men had to come from 2-0 down on the final day of the campaign to beat Aston Villa and were again guilty of a slow start.
Salah was the provider for the opening goal as he laid Thiago Alcantara’s crossfield pass back to the edge of the box and Alexander-Arnold smashed in off the post with the aid of a slight deflection off Dias.
City had played just two pre-season friendlies to Liverpool’s four and took half an hour to find their feet.
Haaland was denied by Liverpool stand-in goalkeeper Adrian with his first sight of goal.
However, the Norwegian should have opened his City account moments later as he failed to properly connect with Joao Cancelo’s inviting cross.
“It’s good for him to see the reality of the new country, new league,” said Guardiola on Haaland’s first taste of English football.
“He was there. Today he didn’t score - another day he will score.”
Nunez was given his chance to shine on the hour mark, but fluffed his first big chance when Ederson prevailed in a one-on-one.
At the other end, City’s new South American striker also got his career in England off to a flying start.
Alvarez’s arrival at the Etihad has gone under the radar in the hype surrounding Haaland.
But the Argentine, who scored six goals in one Copa Libertadores match in May, is also regarded as one of the world’s most exciting young forwards.
Alvarez was quickest to react to the rebound after Adrian saved Phil Foden’s initial effort and the goal stood after a VAR review for offside.
It needed another the intervention of VAR for Liverpool to restore their lead seven minutes from time.
Referee Craig Pawson pointed to the spot after seeing a replay of Nunez’s header coming back off the arm of Dias.
Salah was deadly as ever from 12 yards as he drilled into the bottom corner despite Ederson going the right way.
Nunez then ended any doubt over the result when he pounced on Andy Robertson’s header across goal.
But City’s miserable day did not end there as Haaland hit the bar with the goal gaping deep in stoppage time.