Two goals from Raheem Sterling, and one from Sergio Aguero, Leroy Sane and Fabian Delph helped City extend their goal difference to and maintain their position at the top of the Premier League.
After scoring twice in City's League Cup win over West Bromwich Albion on Wednesday, Sane put City ahead when he played a one-two with David Silva, poked the return ball over defender Scott Dann, and placed his finish between the goalkeeper's legs.
"Shall we score a goal for you?" the home fans chanted, and well they might, with Pep Guardiola's side having now scored 16 goals in three Premier League games.
Crystal Palace will be desperate for at least a point to get them up and running but to do that, they're going to have to score, which has proved impossible for them so far. The former England manager had been tipped as De Boer's replacement prior to the Dutchman actually leaving Selhurst Park and he was quickly appointed as the man tasked with changing Palace's fortunes on the pitch.
With a little over 10 minutes remaining of the half, the lively Sane cut the ball back to Sergio Aguero for a simple tap in but the Argentinian mistimed his shot and it ballooned over the crossbar.
The England striker almost had his second of the afternoon three minutes later when Hennessey could only push away a cross from De Bruyne and Sterling put his opportunity into the side netting.
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It threatens to get even worse for Palace, which must play Manchester United, Chelsea, Newcastle and Tottenham in four of its next five fixtures.
In an attempt to keep the bigger clubs interested, the Football League has allowed English teams playing in European competition to be exempt until the third round since 1996."We have a lot of games".
Romelu Lukaku scored in his sixth successive league game in the first half, only for Saints to improve in the second and have chances to take a share of the points.
Man of the match: LEROY SANE -- scored a superb opening goal, made two others, and a devastating threat throughout the match. "Hopefully, it is just a kick".
Liverpool are 20/1 to finish at the Premier League summit and 10/11 for a top-four finish.
Harry Kane scored twice as 10-man Tottenham held off a West Ham comeback Saturday to maintain its ideal away record with a 3-2 victory in the Premier League.
Spurs were 3-0 up after two goals from Harry Kane and one from Christian Eriksen, but saw Serge Aurier sent off for two yellow cards and had to withstand a late Hammers rally at London Stadium.
But headers from Javier Hernandez and Cheikhou Kouyate either side of Serge Aurier's dismissal ensured an uncomfortable finale for the visitors.