Manchester City s Erling Haaland celebrates after scoring his side s opening goal during the Champions League soccer match between Manchester City and FC Copenhagen at the Etihad stadium (AP)
Haaland now has 19 goals in 11 competitive games for City and was denied the chance of a fourth hat-trick in five home games after being rested for the second half by Pep Guardiola.
City were already 3-0 up at the break as the Norwegian twice swept home from close range before David Khocholava deflected Sergio Gomez's shot into his own net.
Riyad Mahrez took advantage of Haaland's absence to score his first goal of the season from the penalty spot before Julian Alvarez rounded off the scoring.
With maximum points from their opening three games, City are cruising towards the last 16 and can seal qualification with two games to spare should they win in the Danish capital in six days' time.
Copenhagen are languishing in mid-table in their domestic league and in manager Jacob Neestrup's second game in charge came to the Etihad with damage limitation in mind.
But for Copenhagen goalkeeper Kamil Grabara, City could easily have surpassed the six goals they smashed past Manchester United on Sunday.
Haaland only had 11 touches before being replaced at the break, but four of them were shots on target.
Guardiola said ahead of the game that the 22-year-old is peerless at his age, even compared to the greats of the game.
Haaland cooly slotted home his 27th Champions League goal in 22 appearances from Joao Cancelo's cross.
Grabara then produced stunning saves to deny Bernardo Silva, Haaland and Jack Grealish.
But Haaland was predictably in the perfect place to pounce on the rebound when he parried Gomez's shot on 32 minutes.
Another effort from the Spanish full-back was heading towards goal when it struck the unfortunate Khocholava and rebounded into his own net.
With the points safely secured, Guardiola took the opportunity to withdraw Haaland with 10 more games to come before the World Cup break in just over a month's time.
Youngsters Rico Lewis and Joshua Wilson-Esbrand were handed their Champions League debuts off the bench as Cancelo and Silva were also given a breather.
But City still added two more goals in the second period as Mahrez responded to Guardiola's call for the Algerian to get back to his best.
Mahrez sent Grabara the wrong way from the penalty spot after Aymeric Laporte had been hauled down.
He then turned creator for Alvarez to grab his first Champions League goal with a simple finish from close range.
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