Nunez's involvement proved crucial. Liverpool took a deserved 21st-minute lead through Trent Alexander-Arnold's shot which clipped Nathan Ake before going in via the far post, but they were pegged back by an improved City after the break.
While £51m summer signing Erling Haaland did not score, fellow new arrival Julian Alvarez did, forcing home a close-range effort after 70 minutes.
Haaland will want to forget his late effort from six yards when he hit the crossbar when faced with an open goal.
"He had chances, two or three in the first half, and one in the end, and always is there," was City manager Pep Guardiola's assessment.
Of the Norway international's glaring late miss, he added: "He is strong, another time he will put it in the net. It happened. It is football. He was there. He had another goal disallowed because the ball was over the line.
"He fought a lot and made the movements. It is good for him to see the reality of a new country and new league. He was there but today he didn't score and another day he will score. He has an incredible quality and he will do it.
"He has had just two weeks, two weeks and a half, and I am really comfortable with what we are seeing since we arrived this season. I am not absolutely concerned. The reality is we have two or three months ahead of us. He is going to help us."
FA condemns 'dangerous, illegal' use of smoke bombs
Later, the Football Association issued a statement after flares had been let off at several stages during the match.
"We are aware of incidents during the FA Community Shield where flares were used in the stands," it read. "The use of smoke bombs or pyrotechnics in a football stadium is dangerous, illegal, and could have severe consequences.
"We can confirm that we are investigating the matter and will be working with the relevant authorities, the clubs and the police to identify the individuals involved and we will take appropriate action.
"This season, the FA, Premier League and EFL announced new measures and stronger sanctions to tackle anti-social and criminal behaviour in football grounds.
"Premier League and EFL clubs have agreed that if their fans are identified using flares in the stadium then those individuals would receive a club ban. We expect the club to also investigate these incidents and to implement the new rules where applicable."