But backed by raucous fans in a club record European crowd of 53,039, Manuel Pellegrini's men held on to seal a historic result.
The atmosphere was one of the liveliest City have produced in the competition and, contrary to suggestions it might set the wrong tone, the fans' now traditional booing of the anthem actually energised the crowd.
It still took time for the game to warm up but after Zlatan Ibrahimovic continued his duel with Joe Hart by forcing the England goalkeeper to tip over his 15th-minute free-kick there were few quiet moments.
PSG, fielding an unfamiliar back three, looked the most vulnerable in defence with Serge Aurier looking particularly shaky.
Aguero started to look lively and shot narrowly wide twice in quick succession, the first from a tight angle and the second with a dipping half-volley.
The Argentinian was presented with an even better chance on the half-hour as he raced onto a Fernandinho pass but was brought down by goalkeeper Trapp.
Spanish referee Carlos Velasco Carballo pointed to the spot but PSG had a double reprieve first as Trapp escaped with a yellow card and then as Aguero put his spot-kick wide.
Aguero's eventful first half continued as went down clutching his knee after landing awkwardly but City anxiety was eased as he got up to continue after treatment.
Thiago Motta was not so fortunate as he limped off with a hamstring injury on the stroke of half-time, forcing PSG to revert to a back four.
Needing a goal, the visitors started the second half well with Ibrahimovic again testing Hart with a thunderous free-kick and Gregory van der Wiel shooting straight at the goalkeeper.
City tried to mount some attacks themselves but were continually thwarted in the final third and had another nervy moment when Hart had to palm over a Thiago Silva header.
As time began to tick away for PSG, behind on away goals, City fans began to grow in confidence to the extent that they taunted Ibrahimovic. The Swede was compared unflatteringly to Andy Carroll and, far from winding up the PSG talisman, he seemed unable to get into the game.
Eliaquim Mangala and Nicolas Otamendi repelled the visitors and City finally broke the deadlock after 76 minutes as the outstanding De Bruyne curled a superb low shot past Trapp.
Aguero might even have increased the advantage moments later but fired narrowly wide from distance.
PSG battled on despite knowing they would need at least two goals but their efforts proved in vain.
Hart made a crucial save from Edinson Cavani and the French side were also denied by an offside flag when Ibrahimovic turned the ball in five minutes from time.
Hart said it was a special moment for the club.
"It's an amazing night for us," he said.
"We've worked hard in this competition. I've been here since the start of this Champions League run and we did struggle to start with but we started to piece together results and this speaks volumes.
"If you can stay in games then quality really does pay," the England keeper said.
"It was a fantastic performance."
Manchester City will be joined in Friday morning's draw by Real Madrid while four teams are in action tonight - Atletico Madrid, 2-1 down from the first leg, host Barcelona, while Benfica, 1-0 in arrears from the first leg, are at home to Bayern Munich.
MAN CITY: Hart, Sagna, Otamendi, Mangala, Clichy, Fernando, Fernandinho, Navas, De Bruyne (Toure 84), Silva (Delph 87), Aguero (Iheanacho 90).
Goal: De Bruyne 76. Subs not used: Zabaleta, Kolarov, Caballero, Bony.
PSG: Trapp, Aurier (Pastore 61), Thiago Silva, Marquinhos, Van der Wiel, Rabiot, Motta (Moura 44), Di María, Maxwell, Ibrahimovic, Cavani.
Subs not used: Kimpembe, Stambouli, Kurzawa, Sirigu, Ongenda.
Man of the match: De Bruyne
Match rating: 7/10
Referee: Carlos Carballo (Spain)
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