Pep Guardiola's side fought their way through a scintillating early PSG surge when they fell behind to Marquinhos' header, glanced in from Angel di Maria's corner after 15 minutes, to dominate after the break and turn this first leg tie in Paris on its head.
City, who had threatened before the break when Phil Foden missed a great chance, were much more positive and got the reward they deserved after 64 minutes when Kevin de Bruyne's menacing cross evaded everyone in the penalty area and drifted beyond motionless PSG keeper Kaylor Navas.
PSG, with Neymar fading and Kylian Mbappe subdued, were ragged and Riyad Mahrez put City in a great position to reach their first Champions League final when his left-foot free-kick went through the wall to beat Navas seven minutes later.
And to complete PSG's misery, former Everton midfield man Idrissa Gueye was rightly shown a red card late on for a dreadful challenge on Ilkay Gundogan.
Man City's dream comes closer
Manchester City have craved triumph in the Champions League as confirmation they are a European superpower - and this magnificent display brings that ambition closer than it has ever been before.
The Premier League leaders had to show all their qualities before finally overpowering their hosts, who ran out of steam after showing real class in the first half, with Neymar and Di Maria pulling the strings.
Ruben Dias and John Stones were prominent as City held firm in the first half, while after the break, as they showed greater ambition, Joao Cancelo and Kyle Walker carried real attacking threat, and the visitors played with enormous maturity as they pinned PSG back in their own half.
Their menace grew throughout and it was no surprise when De Bruyne levelled then Mahrez put them ahead - indeed PSG ended so beaten and disorganised they may almost feel grateful they only lost 2-1.
City's Champions League history is littered with disappointments in the latter stages of the tournament, often mired in tactical confusion or ill-luck - not so here.
Those experiences mean they will take nothing for granted when this dangerous PSG side come to Etihad Stadium in six days but City have never been in better shape to reach a Champions League final.
PSG still pose a threat - but City in charge
PSG showed in the first 45 minutes exactly why nothing can be taken for granted by City. But former Spurs manager Mauricio Pochettino will know his side are underdogs in the fight to face either Chelsea or Real Madrid in the final in Istanbul on 29 May.
It took all of City's resolve and character to ride out PSG's first-half storm, with Neymar outstanding and while Mbappe was a surprisingly marginal figure, they still have the capability and danger to turn the tables on City at Etihad Stadium.
What will disturb PSG, another club chasing the Holy Grail of a first Champions League crown, is the manner in which City dictated terms to them in the second half, depriving Neymar and Mbappe of any service.
And to add to their troubles they lost their discipline, exemplified by Gueye's reckless late challenge on Gundogan which made a red card a formality.
Manager reaction - 'Sometimes you need to be more relaxed'
Manchester City boss Pep Guardiola to AfroSky Sport: "Sometimes you need to be more relaxed and be ourselves. The first half is normal - you don't want to lose the ball [so] you don't play free. We changed a little in the way we press. We were passive [earlier on]. Then we were more aggressive. It's not easy against Mbappe, Neymar, Di Maria.
"Afterwards we found goals and could have scored another. I'm so satisfied with the performance but we're only halfway. There are 90 more minutes. Anything can happen.
"We didn't have good possession in the right positions. This club don't have much experience in the semi-finals of this tournament. This will help us. In the second half we were aggressive and played really good.
"Against Dortmund, we conceded and came back. Today the same. [We were] ourselves in the second half. We are good playing in a certain way - we can't do a different way."
PSG boss Mauricio Pochettino to AfroSky Sport: "There were two different halves - we did well in the first half but it is difficult to eliminate a team like City. We deserved to be ahead but they were better than us and dominated the second half. The two goals were accidents, but they created more than us. It was one half for each team.
"The two goals are very disappointing. It is difficult to accept but that can happen, and it has happened in a semi-final. It is very painful.
"It is difficult to explain why they were better but we were better in the first half. It was difficult to cope, their physical condition, they were more aggressive. We didn't show the energy you need. The red card could be yellow, could be red.
"The second leg - in football you need to believe. They have the advantage."
