A repeat of the first leg scoreline sees Pep Guardiola's side seal seamless progression to the last eight with a 6-2 aggregate success, helped largely by two early goals this evening.
Manuel Akanji and Julian Alvarez both found the net inside the opening 10 minutes, with Copenhagen goalkeeper Kamil Grabara playing a huge role in letting Alvarez's tame effort squirm through his fingers.
Former Southampton wide man Mohamed Elyounoussi briefly gave the visitors the smallest glimmer of hope just before the half-hour mark, before Erling Haaland restored the two-goal lead in first-half injury time, as the holders cruise past the Danes.
Tonight's win means Man City are now just the third club in Champions League history to win 10 consecutive matches in the competition, after Real Madrid and Bayern Munich.
For Copenhagen, it extends a miserable record away to English sides in the competition, as they are still yet to taste success on eight previous visits.
The Danish side's long wait for an away win in the Champions League also goes on, with their last coming almost seven years ago against Club Brugge in the group stage.
Making seven chances from the side that beat Manchester United in the derby on Sunday, Guardiola's somewhat surprisingly still handed starts to Haaland, Rodri and Ederson, but there was no doubt the crucial encounter against Liverpool at the weekend played a part in the manager's team selection.
One of the players who came into the side from the weekend was involved in both of City's early goals, as it was Alvarez's corner which was met ferociously on the volley by Akanji, leaving Grabara with no chance inside five minutes to settle any lingering nerves.
Just four minutes later, the tie was over, as an Alvarez corner from the opposite side found Rodri, and after he cannoned a header off the crossbar, the ball found its way back to the Argentine, and a rather a tame effort was inexplicably spilled into the back of his own net by Grabara.
After such a woeful start, Copenhagen loosened the shackles slightly and applied a more offensive approach for the remainder of the first half, and that reaped its rewards as the visitors found a consolation strike.
Elyounoussi's long winding run through the City team saw him play a fine one-two with Orri Oskarsson on the edge of the area, before taking the ball in his stride and slotting competently beyond Ederson in the home goal.
A few set pieces and half-chances came Copenhagen's way, but City remained largely in control, and their two-goal lead was restored shortly before the break thanks to yet another European goal for Haaland three minutes into first-half stoppage time.
Rodri's searching ball was controlled excellently by the Norwegian, and he held off the challenge of Elias Jelert before firing back across goal, leaving Grabara stranded and City on the cusp of the last eight.
The comfortable scoreline saw Guardiola replace Rodri at the break, and take Ruben Dias off with a suspension looming should he pick up another yellow card, but there was a nasty looking injury for Matheus Nunes, who looked to have dislocated his finger midway through the second half.
Copenhagen had the best of a relatively quiet second half, as Oskarsson was unable to make contact on Denis Vavro's dangerous delivery, before Ederson smartly denied Magnus Mattsson after some fine footwork from substitute Roony Bardghji.
Rico Lewis almost put some gloss on the scoreline late on for the hosts, but his deflected effort bounced back off the woodwork in injury time, as the match ended 3-1 to the Citizens.
City knew the job was done at half time though, and while the performance was below par in the second period, there was no doubting their dominance across the tie, as they go into the hat for quarter-finals.
Attention now turns to that huge encounter at Anfield against Liverpool on Sunday for City, while Copenhagen host Lyngby as they look to close a three-point gap to Danish league leaders Midtjylland.