While City made it four wins out of four, the Gunners were condemned to a second straight loss in Manchester, having been beaten by United before the international break.
"Emmanuel was outstanding today," City manager Mark Hughes said. "He is an outstanding talent and the best in the world at what he does."
Anderson scored his first Manchester United goal as the champions came from behind to win 3-1 at Tottenham, while Florent Malouda's stoppage-time goal saw Chelsea rally for a 2-1 win at Stoke.
After opening the season with five wins (15 points), Chelsea have a three-point lead over United, City and Spurs at the top of the standings.
goal difference
Liverpool are three points adrift of the trio, who are split by goal difference, after Yossi Benayoun scored a hat trick in a 4-0 rout of Burnley.
"To be top of the league is very important. We have good confidence in our play and a very good atmosphere in the dressing room," Chelsea manager Carlo Ancelotti said. "We are doing very well and want to continue in this good position for as long as we can. We have a very good squad."
Adebayor and Kolo Toure appeared for City against Arsenal for the first time since their big-money offseason transfers from the Gunners. Adebayor was loudly booed by visiting fans as Arsenal dominated early on, but it was the Togo striker's new side that took the lead.
Micah Richards met Gareth Barry's cross with a looping header that hit the post, but goalkeeper Manuel Almunia diverted back into his own net.
Arsenal were more of a threat after the break when Tomas Rosicky replaced Denilson, and the Czech international collected Bacary Sagna's short pass and fed the ball calmly through to Robin van Persie to equalise in the 62nd minute.
celebrate
City were back in front 12 minutes later when Richards squared to Craig Bellamy, who swept the ball home.
Adebayor was booked after his headed goal for racing the full length of the field to celebrate right in front of the Arsenal fans.
"I'm very sorry for all this. Sometimes, the emotion takes over," Adebayor said. "I was very happy to score the goal. Before the game, people have been saying and writing things and the emotions took over. People who love me and know me know how I behave."
City's lead survived a frantic conclusion which saw Shaun Wright-Phillips score a fourth before Rosicky pulled one back.