A £21.2 million signing from Barcelona earlier this week, Pedro scored Chelsea's opener and created a goal for Diego Costa as Jose Mourinho's side went 2-0 up at The Hawthorns.
Having earlier missed a penalty, James Morrison scored twice in response, but despite captain John Terryʼs red card for a last-man foul, Cesar Azpilicuetaʼs first league goal proved enough to give Chelsea a first victory of the Premier League season.
Asked for his thoughts on Terryʼs dismissal, Mourinho told Sky Sports: “I prefer to have no views. I prefer to try to keep quiet.
“I know many people are disappointed with this result. People love Chelsea to lose again. Iʼm so happy the players got what they deserve.
“Four points in three matches is not enough. The feeling is we are fighting against a lot. But today we won.”
At Goodison Park, both sides hit the woodwork either side of half-time, with Romelu Lukaku skimming the crossbar from an Everton free-kick and David Silva rattling the post for City.
Lukaku had earlier seen a goal ruled out for offside, but it was City who took the lead on the hour.
Raheem Sterling glided into the Everton box from the left and slipped a pass to the overlapping Kolarov, who deceived Tim Howard with a near-post finish from an almost impossible angle.
After Vincent Kompany had cleared a header from Gareth Barry off the line, Nasri sealed victory in the 88th minute by playing a one-two with Yaya Toure and neatly lobbing Howard.
“I am very satisfied because it was a difficult team,” said City manager Manuel Pellegrini.
“I think we were very confident and solid in the whole game, so it was difficult for Everton to create chances.”
Victory saw Pellegrini's side complete a sequence of nine league wins and left them as the only side in the top flight with three wins to their name.
In Sunday's other game, Watford and Southampton were both left waiting for a first win after a drab 0-0 draw at Vicarage Road.
The best chance of a poor game fell to Watford midfielder Etienne Capoue, but he headed over the bar from close range.
On Monday night (August 24), Arsenal and Liverpool had to settle for a point each after a richly entertaining game of two halves beneath the Emirates Stadium drizzle implausibly finished 0-0 .
With Arsenal centre-backs Per Mertesacker and Laurent Koscielny absent – the former ill, the latter laid low by a back problem – Liverpool dominated the first half, hitting the woodwork twice and seeing Petr Cech produce an astonishing save to deny Christian Benteke, although Aaron Ramsey also had a goal contentiously ruled out for Arsenal.
The hosts took control in the second half, Alexis Sanchez striking the post, but Liverpool held firm for a result that left them two points below leaders Manchester City and three points above Arsenal.
“I thought we were outstanding. We showed everything. You heard Petr Cech getting a round of applause for the saves he made,” Liverpool manager Brendan Rodgers told Sky Sports.
"Overall we kept a good clean sheet, but weʼre disappointed we didn't win.”
Meanwhile, Manchester United's winning start to the Premier League season ended on Saturday (August 22) as they were held to a frustrating 0-0 draw by Newcastle United at a sun-soaked Old Trafford.
The hosts, who gave Bastian Schweinsteiger a full debut, dominated the early stages and Wayne Rooney saw a goal ruled out for a tight offside, but Newcastle went close when Aleksandar Mitrovic headed against the bar.
Louis van Gaal's side laid siege to the Newcastle goal in the second half, Tim Krul saving from substitute Javier Hernandez and Chris Smalling heading against the post, but Newcastle debutant Florian Thauvin was inches away from toeing in a late winner at the other end.
“We can be satisfied with the performance, but not with the result. We were unlucky,” said Van Gaal, whose side have scored only two goals in their three league games to date.
“We did not make the right choices in the final third, but we played fantastic as a team. I like these kind of games when we work like this, but not this result.
“The performance was one of the best in my period, but we don't reward ourselves. There was only one club that wanted to win and that was us.”
Elsewhere, Leicester City were held to a 1-1 draw at home to Tottenham.
Delle Ali headed in a cross from Nacer Chadli to give Spurs an 81st-minute lead at the King Power Stadium, but within a minute Riyad Mahrez had cut in from the right and curled home his fourth goal of the season to level.
“I am happy. My players have a fantastic spirit. It was an outstanding goal and Riyad Mahrez is a very good player,” said Leicester manager Claudio Ranieri.
Callum Wilson plundered a hat-trick as promoted Bournemouth won 4-3 at West Ham United to claim a first ever top-flight victory.
Wilson exploited a pair of errors by Aaron Cresswell to score twice in the opening 28 minutes, only for a Mark Noble penalty and a Cheikhou Kouyate rebound to draw West Ham level early in the second period.
But substitute Marc Pugh restored Bournemouthʼs lead and Wilson completed his hat-trick from the spot after Carl Jenkinson had been sent off, before Modibo Maiga hit back for West Ham.
“Itʼs a fantastic day on a personal note, but the important thing is we got the three points,” Wilson told BBC Sport. “In the first two games I think there were nerves, but today I felt we showed real confidence.”
Meanwhile, debutant Bakary Sako struck in the 87th minute to give Crystal Palace a 2-1 win at home to Villa, who had been in line for a point after a Pape Souare own goal cancelled out Scott Dannʼs header.
Bottom club Sunderland stopped the rot after two straight defeats by drawing 1-1 at home to Swansea City, with Jermain Defoe equalising for the hosts after Bafetimbi Gomis had scored his third goal of the campaign.
Record signing Xherdan Shaqiri created an early goal for Mame Biram Diouf on his Stoke City debut, but his side had to settle for a 1-1 draw at Norwich City due to Russell Martin's 28th-minute equaliser.
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