The Portugal winger broke clear from the halfway line in the fourth minute of time added on to follow up his sublime equaliser earlier in the second half.
City had capitalised on David de Gea's hesitancy to go ahead through Joleon Lescott and Edin Dzeko but Chris Smalling halved the deficit after the break.
Nani told Sky Sports 1: "This is United, we all believe until the last minute and the attitude of the lads in the second half was that everyone believed we could score.
"It is good to play against Man City and win like that. I think our fans today will be so proud of us, it is a beautiful day to enjoy."
Asked about his winner, when he rounded Joe Hart before sliding the ball into an empty net, Nani said: "I tried to chip it but the keeper stayed on his feet, so at the last second I changed my mind."
United striker Wayne Rooney admitted the win was sweeter because of the opposition.
"Of course," he said. "Obviously they are going to try to fight us for that (Premier League) title. They scored two goals from nowhere but we showed character to win the game."
United boss Sir Alex Ferguson was reluctant to criticise De Gea for the second City goal.
He said: "Well it was bending a little bit...it's difficult to say."
The Scot added: "I certainly thought our performance throughout was very good in terms of the football. I couldn't believe we were 2-0 down at half-time after it looked to me like we were controlling the game.
"But credit to the players, they kept their heads, played football and got the result we deserved."
City boss Roberto Mancini believes his side must learn important lessons from the defeat.
Asked if it was a big opportunity wasted, he told Sky Sports News: "Yes because we went two-nil after 45 minutes.
"But this is football. Second half probably we didn't play very well and United scored two goals in seven minutes.
"But probably the correct result was 2-2 and go on to penalties but that is it."
He did not believe United would hold a psychological edge after the win.
"I think that this is only one game. It is not important for the Barclays Premier League, for the FA Cup," he added.
"It is an important game because it is the first game and we wanted to win this game but if you play against United you can lose because they play well.
"When you go up two-nil I think you need maybe to control the ball and the game because a game like this can change very suddenly."
He believes his side can overhaul United and win the Premier League - but must learn from their mistakes.
"I repeat if we understand why (we lost) it will be very important."
Ferguson, meanwhile, has promised Nani he will start United's opening Premier League game at West Brom next Sunday.
Nani bagged a brilliant brace and had a much better experience than the one he endured at Wembley just over 10 weeks ago, when he was left out of United's starting line-up by Ferguson and then gifted Barcelona their killer third goal in the Champions League final.
And the 24-year-old's reward will come at The Hawthorns where he will be a central figure as United begin the defence of their title.
"Nani had a fantastic season last year," said Ferguson. "He contributed 18 assists and scored nine goals.
"He was unfortunate that Antonio Valencia came in at a time when we needed a bit of freshness and a boost to the squad.
"But you have seen Nani's form in pre-season and again today. He will start the season."
Nani was just one of United's stand-out performers.
Rooney was a figure transformed from 12 months ago, whilst Ashley Young enjoyed a memorable debut and Cleverley provided the attacking thrust Ferguson was hoping for when he was introduced, along with Phil Jones and Jonny Evans, at half-time.
"We toyed with the idea of starting Cleverley," revealed Ferguson.
"I thought Michael Carrick's experience would be better suited to the game but we were always going to bring Cleverley on.
"I didn't know exactly where I could have played him but at 2-0 down, I knew Cleverley could get forward from midfield.
"We needed that type of player."
The result leaves Ferguson in optimistic mood ahead of the opening weekend, although the United boss is refusing to take anything for granted.
"I trust them and have confidence in the ability of the players but you can never be confident in the Premier League," he said.
"It is such a difficult league. Six teams could be challenging for the title."
Since Mancini arrived at City, derby matches have tended to be close.
However, much to Mancini's chagrin, the Blues were unable to consolidate their position of strength after the break.
"I don't think it has given United a mental edge but it will be important for us to know why we lost this game," he said.
"A top team doesn't always play well, but when we score two goals and go 2-0 up, we need to have a strong mentality.
"If we play another strong squad like United, or against someone like Real Madrid in the Champions League, we need to continue to play football.
"We need to stay high up the pitch, not go too deep like we did in the second half."
Source: Team Talk
Source: Team Talk