The Gunners moved aboveLiverpool after PFA Player of the Year nominee Cesc Fabregas inspired asecond-half revival with a superb 25-yard effort, before Julio Baptista wrapped things up late on.
Afterwards Gunners boss Arsene Wenger admitted Arsenal had to work hard for the victory. He said: ‘‘We didn't expect City to get back to 1-1 after we took the lead but we had to wait for the win.
‘‘I think we deserved the victory as we created a lot of chances and when we got our second it made it easier because they had to change their shape.
‘‘But now we must try and build on this and win as many points as we can.’’
The home side broke through in the 12th minute, after Abou Diaby won a crunching tackle 30 yardsout, and took the ball to the edgeof the box before pushing itwide to Emmanuel Eboue on the right.
The full-back whipped over a teasing cross through the six-yard box, Nedum Onuoha hesitated at the far post and Rosicky stole in to volley his second goal of the week.
With 23 minutes gone, there was a lengthy stoppage as Diaby had to be patched up after receiving a nasty gash above his eye following an accidental boot in the face from City skipper Richard Dunne as the Arsenal man slid into a tackle. Despite the best efforts of the Arsenal medical staff, Diaby was unable to continue further after battling on bravely for a few minutes.
Baptista, on-loan from Real Madrid, replaced the Frenchman after half an hour.
The visitors levelled in the 41st minute. Goalkeeper Jens Lehmann made a hash of his clearance, and Barton fed Michael Johnson — who weaved to the edge of the penalty area to set up Beasley for a cool finish.
The Gunners went on the offensive in the second half and eventually took the lead in the 73rd minute.
City failed to clear their lines, and as the ball dropped to Fabregas some 25 yards out, the Spain midfielder sent a brilliant strike past Isaksson for his second goal of the week.
Then Alexander Hleb weaved into the right side of the area and stabbed the ball towards the penalty box, where the brazilian Baptista clinically swept it into the bottom corner.
Lehmann, Eboue, Toure, Gallas, Clichy, Hleb, Fabregas (Denilson 85), Silva, Rosicky (Senderos 90), Diaby (Julio Baptista 30), Adebayor.
Isaksson, Onuoha, Dunne, Distin (Corradi 78), Ball, Jihai (Samaras 78), Hamann, Barton, Johnson, Beasley, Vassell (Ireland 90).
M Halsey (Lancashire).