Pep Guardiola hails dazzling Kevin De Bruyne as City cruise through Copenhagen
De Bruyne's early opener was cancelled out against the run of play by Magnus Mattsson.
Bernardo Silva restored City's lead before half-time, but they had to wait until stoppage time to add further punishment for the hosts when Phil Foden turned home De Bruyne's cut-back.
De Bruyne was sidelined for five months by a hamstring tear suffered on the opening night of the Premier League season in August.
But since his return last month, the midfielder has scored two goals and provided seven assists in seven appearances.
"Extraordinary," said Guardiola of De Bruyne's statistics. "The biggest players love to appear in the biggest stages.
"It's the hour of truth when you are in the last 16 of the Champions League and we start well."
The English champions have now won 11 consecutive games in all competitions as they remain on course to repeat last season's treble of Champions League, Premier League and FA Cup.
Copenhagen had not played a competitive game for two months since sealing their place in the last 16 by dumping out Manchester United and Galatasaray in the group stages.
"They had a great group stage so we had to respect them," said De Bruyne. "We started really well but I think we made one mistake and they pounced on it.
"We played a really good game. In the second half we created a lot of chances, could have scored more and luckily in the end we scored the third one, so it is a little bit of an advantage now."
Grealish injury blow
That lack of match sharpness from the Danish champions showed in the early stages as City stormed out of the blocks.
De Bruyne headed a glorious chance wide and Kamil Grabara denied Ruben Dias with a fine save inside six minutes.
The former Liverpool goalkeeper had no chance when De Bruyne broke the deadlock on 10 minutes with a clinical low finish from Foden's pass.
Jack Grealish had been surprisingly handed just his second start of the year by Guardiola, but the England international lasted just 15 minutes before he pulled up with a suspected groin injury.
City had enjoyed nearly 80 percent possession and barely let Copenhagen inside their half for the first 35 minutes, yet were made to pay for one moment of sloppiness.
Ederson's poor clearance was straight into the path of Mohamed Elyounoussi and his blocked shot fell to Mattson to mark his debut with a stunning strike from outside the box.
City regained their composure and the lead before half-time.
Mattson was unfortunate as his attempted clearance ricocheted off De Bruyne and perfectly into the path of Silva to flick beyond Grabara.
The Copenhagen goalkeeper kept his side in the tie in the early stages of the second period with spectacular stops to deny De Bruyne and Doku.
Grabara then twice won a head-to-head battle with Haaland in stoppage time.
City were keen to build up a comfortable advantage with the second leg falling between crucial Premier League games against Manchester United and Liverpool next month.
And they finally got the third goal that should kill off the tie when the in-form Foden slammed home his 15th goal of the season as City extended their unbeaten run in European competitions to 21 games.