Goals from Kevin De Bruyne, Kelechi Iheanacho, Raheem Sterling and Ilkay Guendogan, on his Premier League debut, wrapped up the points after another scintillating display from the title favourites who continue to lay down a marker to their rivals.
Heading the chasing pack are Everton, who stayed two points behind City with a 3-1 home win over Middlesbrough, Gareth Barry marking his 600th league appearance with a goal.
Arsenal made it three successive league wins for the first time since January when they eased past 10-man Hull City 4-1 with Alexis Sanchez scoring twice and missing a penalty.
There was also a double strike at Leicester City where new signing Islam Slimani enjoyed a league debut to remember as the champions rediscovered their domestic form to beat Burnley 3-0.
Some pundits predicted Manchester City might suffer during Sergio Aguero's three-match suspension but, after winning the Manchester derby last weekend, they tore into Bournemouth and wasted little time in taking the game away from their opponents.
City were 1-0 up after 15 minutes when De Bruyne cleverly fired a free kick beneath the wall and into the net. They doubled the lead 10 minutes later when Iheanacho stabbed the ball home.
The Nigerian then turned provider for Sterling soon after halftime and Guendogan rounded off the scoring when he drilled the ball low inside the post.
There was a sour note for City when they had Spaniard Nolito sent off for a head-butt with four minutes remaining.
That did little to dampen the spirits of Guardiola, however, who heralded another superb display from Belgium playmaker De Bruyne.
"We are so lucky we have Kevin with us," the coach said. "It was a fantastic performance."
Everton trailed against Middlesbrough following an own goal by keeper Maarten Stekelenburg before Barry levelled.
Further first-half goals from Seamus Coleman and Romelu Lukaku then gave Ronald Koeman the best five-game start to a Premier League season by an Everton manager.
FIRST TASTE
It was a day of superb individual displays with Slimani whetting the appetite of Leicester fans with two goals.
Slimani, who made his debut in the Champions League in midweek after costing a club record 29 million pounds ($37.70 million) last month, was handed his first taste of Premier League action and scored twice in four minutes either side of halftime.
The Algeria striker met Christian Fuchs' inswinging free kick in first-half stoppage time and then headed home after the break when Riyad Mahrez showcased his dancing feet to shimmy into the box.
Ben Mee's own goal completed the scoring late on as Leicester took their haul to seven points from five games.
Arsenal's season has yet to fully ignite but they made light work of a Hull side who had Jake Livermore sent off for handball in the first half.
Sanchez deflected the ball home to put Arsenal ahead after 17 minutes but the Chilean had his penalty saved by Eldin Jakupovic following Livermore's dismissal.
It was plain sailing from there on in, though, as Theo Walcott doubled the lead 10 minutes into the second half and, although the hosts pulled a goal back from the penalty spot through Robert Snodgrass, there was to be no late fightback.
Sanchez rifled the ball high into the net and Granit Xhaka made it 4-1 with a bullet finish from distance in stoppage time, putting the London club third in the table on 10 points.
West Bromwich Albion midfielder Nacer Chadli marked a superb home debut with two goals, one a penalty, and two assists as they beat hapless West Ham United 4-2 to hand the Londoners a third straight league defeat.
($1 = 0.7692 pounds)
(Editing by Tony Jimenez)
