Pep Guardiola's side recovered from Theo Walcott's early opener as second half goals from Leroy Sane and Raheem Sterling delivered the knockout blows.
Pep Guardiola's side recovered from Theo Walcott's early opener as second half goals from Leroy Sane and Raheem Sterling delivered the knockout blows in a heavyweight clash at Eastlands.
City's second win in five days lifted them into second place and closed the gap on leaders Chelsea to seven points ahead of the busy Christmas period.
"At half-time I told them not to think about the score, I told them to keep going. Arsenal were lucky in the first half," Guardiola said.
"The guys give everything in every game. I'm happy to be City coach. In terms of spirit it's always there."
Just days after squandering the lead in a late loss at Everton, Arsenal's second successive defeat leaves the fourth placed Gunners languishing nine points behind Chelsea as their 14-match unbeaten run suddenly becomes a distant memory."
"Of course I'm disappointed and frustrated. We had a very good first half and then we conceded two offside goals," Arsenal manager Arsene Wenger said.
"It's difficult to accept. I believe there's a lot going on (regarding refereeing decisions). It's hard going into game like that and get decisions go against you."
Guardiola's latest stab at finding the right formula in City's creaky defence saw the Spaniard again leave out John Stones and deploy full-back Aleksandar Kolarov alongside Nicolas Otamendi.
But it took Arsenal only five minutes to expose City's soft centre as Alexis Sanchez caressed a fine pass behind Otamendi to Walcott, who dispatched a cool finish past Claudio Bravo from close-range.
Showing impressive composure, Guardiola's team monopolised possession after that and Sterling almost equalised when he headed just wide from Kevin de Bruyne's cross.
City's territorial dominance was rewarded in the 47th minute when David Silva's pass picked out Leroy Sane and the German winger beat the offside trap to slot home.
Unable to stem the tide, Arsenal needed a series of saves from Petr Cech to keep them level, but the Gunners defence was finally breached again in the 71st minute when England forward Sterling beat Cech at his near post.
While Arsenal stumbled, their north London rivals Tottenham battled back to defeat Burnley at White Hart Lane.
Burnley stole the lead against the run of play in the 21st minute when George Boyd's cross came off Moussa Dembele and Ashley Barnes was alert to convert his side's first away league goal in open play this season.
But Mauricio Pochettino's men were level five minutes later through England midfielder Dele Alli, who made a well-timed run to meet Kyle Walker's cross with a lethal finish.
Tottenham's winner arrived in the 71st minute when Moussa Sissoko's found Rose in space and the England left-back smashed home at the near post to move his fifth placed team within one point of the top four.
"We knew Burnley are a team that fights a lot, but we played in a very good way and fully deserved the victory," Pochettino said.
Elsewhere on Sunday, Southampton forward Jay Rodriguez bagged a brace to inspire his side's 3-1 win against local rivals Bournemouth.
Rodriguez hadn't scored in the league since August but he ended that barren stretch with a second half double in the south coast derby at Dean Court.
Claude Puel's team had fallen behind to Nathan Ake's early opener, but Ryan Bertrand levelled soon after to set the stage for one of the better days in recent memory for the injury plagued Rodriguez.
Southampton's second win in their last nine away league matches lifted them into seventh place, while Bournemouth remain in mid-table.