Haaland's first-half brace was followed by a Davit Khocholava own goal, a Riyad Mahrez penalty and a tap-in from Julian Alvarez as Pep Guardiola's side eased to victory at the Etihad Stadium.
That makes it 19 goals in 12 games in all competitions for the former Borussia Dortmund star after his hat-trick in the 6-3 derby win over Manchester United.
City has a 100 per cent record in Group G after three games and needs just two more points to seal its place in the last 16.
Haaland opened the scoring inside seven minutes, slamming home Joao Cancelo's low cross with his right foot.
But for the impressive shot-stopping of former Liverpool academy goalkeeper Kamil Grabara it could have been far worse for Copenhagen in the first half, though his parry of Sergio Gomez's shot was tapped in by Haaland for City's second just after the half-hour.
It was three before the break after Gomez's shot from the edge of the box took two deflections, the second of which, off Khocholava, bounced into the net.
Haaland was subbed off at half-time, which may well have irked him considering he would have had a chance at another hat-trick when City were awarded a penalty early for Marko Stamenic's foul on Aymeric Laporte.
It was the left foot of Mahrez, not Haaland, which sent Grabara the wrong way from the spot.
Guardiola gave youth a chance as City cruised in second gear, with Alvarez on hand to make it five after a neat run from Jack Grealish ended in Mahrez supplying the striker with a simple finish.