Haaland wasted no time in getting City going with yet another strike in his remarkable campaign, sweeping home an early opener before putting the game beyond the Danish side inside 32 minutes.
City kept coming and added a third six minutes before the break as David Khocholava put through his own net, with Haaland lurking just behind in the hunt for his second treble in four days.
There was to be no hat-trick for Haaland as he was withdrawn at halftime, but the goals kept coming as Riyad Mahrez slotted home a penalty before Julian Alvarez finished things off with a late fifth.
The most comfortable of victories ensured City have taken a maximum of nine points in the group and needed two more to be sure of a spot in the knockout stages.
Copenhagen are bottom on one point from three games.
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