Pep Guardiola's side comfortably swept the Danish champions aside in their Champions League last 16 clash, beating Jacob Neestrup's side 3-1, to seal a 6-2 aggregate win.
Manuel Akanji got the ball rolling, before Julian Alvarez's effort was spilt into the back of his own net by visiting goalkeeper Kamil Grabara.
After going two-up inside 10 minutes, the hosts allowed Copenhagen a tiny glimmer of hope, when Mohamed Elyounoussi pulled one back, but Erling Haaland completed the scoring in first-half injury time, as the Citizens sealed safe progress into the quarter-finals
Guardiola made seven changes to the side which beat Manchester United in the derby last weekend, with the tie hugely in their favour following the first-leg win.
One of those changes was enforced though, as Jeremy Doku was ruled out of the match shortly beforehand due to injury.
"He had some muscular problems so we did not want to take the risk," Guardiola revealed pre-match, putting his fitness into doubt ahead of the trip to Anfield.
There was an additional injury worry for City during the match too, as Matheus Nunes was forced off with a gruesome finger injury in the second half.
Following an innocuous off-the-ball incident, Nunes suddenly appeared in great distress, pleading urgently for the assistance of the medical staff.
A brief close-up of the incident showed that Nunes had seriously injured his finger in what appeared to be a severe dislocation.
The City physios came to his aid, popped it back into place and quickly bandaged up his hand, but the Portuguese midfielder still seemed in some pain following the full-time whistle, and could face some time out the side.
Among those given surprise starts were Rodri and Haaland, and more eyebrows were raised when the Norwegian was kept on for 88 minutes, but both got through the encounter unscathed.
Rodri was replaced at half time with Man City four goals to the good on aggregate, but Guardiola claimed post-match that he left Haaland on because he wants the striker to build rhythm, following his recent injury layoff.
Given City's comfortable position on the night, Kevin De Bruyne, Phil Foden, Nathan Ake and Bernardo Silva were all unused substitutes, meaning they should be fit and ready to go at Anfield at the weekend.
Alvarez was given a rare recent start, after three straight substitute appearances, but he still faces a battle to break back into the side, despite a goal and assist tonight.
Elsewhere in the City squad, Jack Grealish remains sidelined, after being forced off in the first half of their 6-2 win at Luton Town in the FA Cup last midweek.