Arne Slot can do no wrong as Liverpool's stand-ins deliver at Leipzig
The win was Liverpool's third out of three in the Champions League and meant they have won their first six games away from home to start the season, a new club record.
Dutchman Slot has won 11 of his 12 games since replacing Jurgen Klopp at Anfield, also a club record.
He appears to have the Midas touch at the moment and even when he is forced to field second-choice players, he comes up trumps, as was the case in Leipzig on Wednesday.
Nunez has been used largely as a substitute this season but an injury to Diogo Jota meant the often-frustrating Uruguayan was handed a start and he took full advantage.
He scored the winner, had a nailed-on penalty turned down and forced a great save from Leipzig keeper Peter Gulacsi in a performance full of energy and endeavour.
Slot was annoyed that his side failed to kill off the game and Liverpool endured some nervy moments in the closing stages with Kelleher, again standing in for the injured Alisson, producing two wonderful saves to preserve his side's lead.
"We are very fortunate. It's also normal at a club like ours to have two very good players in every position," Slot said.
"We are happy that we have two excellent goalkeepers. But it's not only him - other players who maybe haven't played that much this season or haven't been starting also showed up today."
Nunez's second goal of the season was a tap-in and Mohamed Salah's header might have been going in anyway.
But it was a reward for an industrious display.
"What I liked from Darwin was that he was also strong, comfortable on the ball, kept the ball a lot, fighting if he had to defend, so he made it a really difficult game for the two centre backs of Leipzig," Slot said.
"And then for him scoring, I think that is always nice for a striker to be on the scoresheet."
Leaders Liverpool now travel to Arsenal for a crunch Premier League game on Sunday when victory would put them seven points clear of a side many tipped for the title.
Salah was spared the last 30 minutes in Leipzig as he was substituted and while the Egyptian looked aghast at going off, even that decision worked out well for Slot.
"We have some injuries now so I have to take good care of the players that have played a lot and Mo is one of them and on Sunday, a big game is coming up again," Slot said.
"So, I need to use as many players as I can use for these next tough weeks and these tough months that are coming up, so that they are all prepared to play."