Goals by Sergio Aguero, Vincent Kompany and Fernandinho were the least City deserved for a dominant display against a side who took 70 minutes to register a shot on target.
While a buoyant City top the table with six points, six goals scored and none conceded, Chelsea have one point after failing to win either of their opening two fixtures for the first time since 1998.
Chelsea's troubles will not have gone unnoticed by Arsenal, who belatedly got their season into gear with a 2-1 derby win at Crystal Palace -- Damien Delaney's own goal sealing their first points of the season.
The sense of unease in the Chelsea camp was increased when talismanic skipper John Terry was substituted at halftime -- the first time he had ever been hauled off by manager Jose Mourinho.
Mourinho later confirmed that Terry had been replaced by pacey central defender Kurt Zouma for tactical reasons.
The Portuguese caused controversy last week when criticising first-team doctor Eva Carneiro for treating Eden Hazard and leaving Chelsea temporarily with nine men in the opening day draw with Swansea City and he faces another testing week.
Mourinho was already on the offensive, though, saying Chelsea's defeat by City had been undeserved.
"The best team in the first half won the game. The best team in the second half was Chelsea for sure," he told Sky Sports.
"Second half everything was different. If the 1-0 was a doubtful result at minute 70, 3-0 is completely fake."
PUZZLING ANALYSIS
Chelsea did regroup well but his analysis was still puzzling.
"It was a comfortable game. To start the way we did today is definitely the right signal but there's still a lot to come," City captain Kompany said.
Chelsea's 2-2 draw with Swansea came a week after defeat by FA Cup winners Arsenal in the Community Shield and was followed by Mourinho's removal of Carneiro from bench duties.
His team needed a response on Sunday but they were outplayed in the opening 45 minutes.
Aguero had already been causing Terry and central defensive partner Gary Cahill headaches and had three sights of goal in the opening 30 minutes before finally putting his side ahead.
The Argentine played a one-two with Yaya Toure in a crowded area, wriggled into space past a lumbering Cahill and fired the ball just inside Asmir Begovic's post.
Eliaquim Mangala should have made it 2-0 when he headed wide as Cahill was flattened by his own goalie. Tempers then flared as Fernandinho's elbow left a furious Costa bloodied.
Hazard had Chelsea's one real chance in the 70th minute but fired a shot straight at Joe Hart before City's defenders cleared the loose ball with Costa lurking.
Kompany's glancing header gave City breathing space before Branislav Ivanovic gave the ball away and Fernandinho completed Chelsea's misery with a clinical finish past Begovic, who could have expected more protection on his first start in place of the suspended Thibaut Courtois.
Arsenal had Alexis Sanchez back in their starting line-up and it was the Chile forward's 55th-minute header that was turned into his own net by Delaney as Arsenal responded to last week's home defeat by West Ham United.
"I'm very pleased with the three points. If we had gone two games and zero points it would be absolutely difficult, we knew this would be a tricky one," Arsenal manager Arsene Wenger said.
Olivier Giroud had given the Gunners the lead with a smart volley in the 16th minute, only for Joel Ward to equalise against the run of play 12 minutes later.
