Armed with a two-goal advantage from the first leg in Denmark, Pep Guardiola’s side wasted little time in strengthening their grip on the tie with two goals inside the opening 10 minutes.
First, Manuel Akanji found a yard of space inside the box to expertly volley home from Julian Alvarez’s corner, before the Argentine doubled City’s lead four minutes later with a powerful long-range effort that squirmed through the grasp of Kamil Grabara.
The hosts continued to dominate proceedings after their quickfire double, but it was Jacob Neestrup’s men who pulled a goal back against the run of play shortly before the half-hour mark.
Mohamed Elyounoussi showed impressive speed to break into the City box, and the Norwegian played a superb one-two with Orri Oskarsson before finishing confidently into the bottom corner.
Undeterred, City restored their four-goal aggregate lead on the stroke of half time, with Erling Haaland rifling home after a pinpoint ball over the top from Rodri.
That goal all but ended Copenhagen’s hopes of an unlikely comeback, and the early stages of the second half were unsurprisingly dominated by Guardiola’s men.
Nevertheless, the visitors refused to go down without a fight, as substitute Magnus Mattsson saw a strike deflected wide and Elyounoussi blasted wastefully over the bar from the edge of the box.
With City using the closing stages as an opportunity to rest several of their key players, the contest ultimately fizzled out, extending the hosts’ unbeaten run in all competitions to 19 matches ahead of a crunch Premier League clash with Liverpool on Sunday.
Copenhagen, meanwhile, remain winless on all eight of their trips to England (D2, L6).
Flashscore Man of the Match: Manuel Akanji (Manchester City)