Bernardo Silva twice benefited from Doku’s work with a brace while Phil Foden, Manuel Akanji and Nathan Ake also got on the scoresheet at the Etihad Stadium.

Luis Sinisterra grabbed a Bournemouth consolation but the only real concern for City was an injury to Haaland, who hit the woodwork early on before hobbling off at half-time.

City, who are already without Kevin De Bruyne for a prolonged period, will hope the problem does not prove serious with games against Chelsea and Liverpool in the coming weeks.

On this occasion, City did not really need the Norway international.

The feelgood factor Bournemouth generated by winning their first league game of the season last week quickly evaporated as City eased through the gears.

It may have taken them 30 minutes to register their opening goal but, such was their dominance, the result rarely seemed in doubt.

Silva sent a dipping effort narrowly over the bar and Rodri shot straight at Andrei Radu.

Haaland went closer when he headed against the post and was then denied by a Lloyd Kelly block before Silva curled just wide.

It was no surprise when the hosts finally took the lead, Doku picking up possession on the edge of the box and playing a one-two with Rodri before curling a shot around Radu.

The second quickly followed with Doku again involved. The Belgium forward combined with Kyle Walker on the right and bamboozled the defence before picking out Silva in front of goal.

Doku thought he put City 3-0 ahead soon after as his mesmeric spell continued. A neat touch opened up a shooting opportunity on the edge of the box and he lashed towards goal.

He ran off to celebrate as the ball found the bottom corner but he was forced to settle for a creator’s role again as replays showed a deflection off Akanji.

Haaland almost added a fourth after being played in by Julian Alvarez but Illya Zabarnyi slid in to block.

That proved his last significant involvement as he ended the first half with an apparent limp and manager Pep Guardiola removed him at the interval.

Dominic Solanke had the ball in the net for Bournemouth after the restart but Ryan Christie was ruled offside in the build-up.

Solanke was unperturbed and rattled the frame of the goal with another effort on the hour but that served only to fire City back up.

Yet again Doku proved the dangerman, cutting into the box on the left and teeing up Haaland’s replacement Foden in front of goal.

Sinisterra pulled one back 16 minutes from time after taking a touch from a sweeping Max Aarons pass and turning home.

Doku was not done, however, and released Silva with a sublime long ball, which the Portugal midfielder raced onto and coolly flicked in.

Ake completed the rout with a stopping header late on.