Pep Guardiola's side proved far too strong for their opponents over the course of the 90 minutes, and the victory has moved them onto nine points in Group G, three ahead of second-placed Borussia Dortmund.
Haaland entered the match off the back of a hat trick in the Manchester derby on Sunday, and it took just seven minutes for the forward to get off the mark against Copenhagen, with the striker finding the back of the net with an emphatic finish inside the box after a smart cross from Joao Cancelo.
The home side had two more chances in quick succession, but Bernardo Silva saw his effort tipped onto the post by Copenhagen goalkeeper Kamil Grabara, who then managed to keep out a header from Haaland.
Grabara had to make another two saves in the period that followed, again keeping out Haaland from inside the box before denying Jack Grealish, who had been looking to pick out the top corner in the 24th minute.
Copenhagen conceded a second in the 32nd minute, though, with Haaland converting from close range after Grabara had palmed an attempt from Sergi Gomez into his path.
Man City then had a third in the 39th minute, with Davit Khocholava turning into the back of his own net after Gomez had drilled a shot into the away side's penalty box.
Silva passed up the chance to make it four in the latter stages of the first period when he found himself inside the box, but Copenhagen were already all but out of the contest at the interval.
The home side did not have to wait too long to make it 4-0, though, with Riyad Mahrez netting from the penalty spot in the 55th minute after Aymeric Laporte had been fouled by Marko Stamenic.
Man City's fifth then arrived in the 76th minute when Julian Alvarez converted after smart work from both Grealish and Mahrez.
Haaland was withdrawn at the interval ahead of a busy run of matches for the Citizens, which prevented the Norway international from having the chance to score another hat trick.
Guardiola's side are eight points clear of third-placed Sevilla in the group with three games left, while Copenhagen are at the foot of the section, boasting just a point from their three fixtures.