Manchester City's Erling Haaland celebrates scoring their first goal v Luton with Kevin De Bruyne and Bernardo Silva
It was the Norwegian's eighth hat-trick for City and he also became the first player to score five in a game twice for the club.
City opened the scoring in the fourth minute when Kevin de Bruyne, who assisted the first four goals, was allowed time and space to cut the ball back for Haaland to convert.
The pair combined again 15 minutes later, with Haaland running on to a through ball before powering it past Luton goalkeeper Tim Krul and it was a similar move that brought the third, only this time with a delicate dink to finish.
Jordan Clark pulled one back for Luton with a stunning strike, curled beautifully into the top corner from 25 yards on the stroke of half-time and gave Rob Edwards' side hope of a memorable comeback with a thumping finish seven minutes into the second half.
However, Pep Guardiola's team soon dashed those hopes when De Bruyne squared for Haaland to tap into an empty net after a superb pass from Kyle Walker had sent the Belgium midfielder clear.
Haaland got his fifth - matching his effort against RB Leipzig in last season's Champions League last 16 - when his low shot went straight through Krul, who then saw a long-range strike from Mateo Kovacic flash past him for the visitors' sixth.
Luton had opportunities in the second half with Stefan Ortega, starting in place of Ederson for City, forced into action a number of times. City might easily have added to their lead at the other end but once Haaland was replaced with 15 minutes to go, there was not the same ruthlessness and the hosts were spared any further punishment.
The one sour note for City was an injury to Jack Grealish, who was forced off late in the first half, but they are now unbeaten in 18 games and remain in pursuit a second consecutive treble.
-- Courtesy of BBC Sport