Despite a confident start, City conceded first-half goals from Theo Walcott and Olivier Giroud to leave themselves a huge task at the break.
In the final analysis the deficit proved too much to overcome, although Yaya Toure gave City hope with an exquisite goal with 10 minutes remaining.
City had struggled to find an attacking edge until that moment, but given a glimpse of a point they proceeded to lay siege to the Gunners goal in the final stages, only for substitute Wilfried Bony and Toure to see further efforts slide narrowly wide.
The leveller did not arrive though and the result continues City’s away day struggles – the Blues have not won on the road in the Premier League since September 12 – and leaves them four points behind Arsenal and six behind leaders Leicester.
The task now for City must be to pick themselves up quickly as the hectic festive fixture list kicks into overdrive.
Manuel Pellegrini’s men face Sunderland (home), Leicester (away) and Watford (away) in quick succession in a spell that can often define a team’s season.
Pellegrini made four changes from the side that eked out the win over Swansea.
Sergio Aguero returned to the starting line up for the first time since injuring his foot against Southampton at the end of November.
Aleksandar Kolarov, Kevin De Bruyne and Fabian Delph were also brought back in with Gael Clichy, Jesus Navas, Raheem Sterling and Bony on the bench.
Delph, deployed on the left side of midfield, had an early injury scare when he overextended going into a challenge.
Thankfully the England man ran it off, and he was a one of the key performers in a strong start for City.
Both sides seemed full of respect for each other in the early exchanges but City were shading it, with De Bruyne threatening with an early run before David Silva lashed a shot high and wide after finding space just outside the box.
Fernandinho was closer with another driven effort shortly after, before fine link up play between Delph, Toure and Silva saw the latter’s shot deflected.
After a wonderfully controlled volley from Silva, De Bruyne fired in a left-footed shot that was blocked, and two minutes late the same player forced Petr Cech into a save down low to his left.
The crowd had a chuckle from the resulting corner as De Bruyne kicked the flag instead of the ball from his first attempt.
The Belgian had a chance to wipe the smiles from the home fans’ faces just after the half-hour but, after fine work from Aguero, he shot inches wide with Silva pleading for the ball in the middle.
City were made to pay for that missed chance moments later when Ozil fed Walcott and the England man whipped an unstoppable shot past Joe Hart’s despairing dive.
City struggled to respond to the setback, although one scooped ball from De Bruyne almost found Aguero in the Gunners’ box, and on the stroke of half-time disaster struck.
Fernandinho couldn’t control Eliaquim Mangala’s strong pass and the ball fell to Walcott. He found Ozil, who set Giroud free down the left to shoot through Hart’s legs.
With a game to chase Pellegrini put Sterling on for Delph, and the winger’s pace stretched the Gunners defence early in the second period.
Aguero shot tamely at Cech, while at the other end Joel Campbell clipped a shot narrowly over from close range after Nacho Monreal’s cross.
The play had a more frantic edge about it as City looked to force their way back into the contest, with Aguero calling Cech into action again with a glanced header from Kolarov’s free-kick.
Moments later Aguero latched onto De Bruyne’s centre, but the result was the same – the ball nestling into Cech’s midriff.
The match was now wide open, and only a brilliant sprawling stop from Hart denied Aaron Ramsey one-on-one.
As he hinted he would in his pre-match interview, Pellegrini took Aguero off just after the hour mark with Bony coming on.
City made their final change with Navas on for Silva but City were struggling to break through.
Bony saw one headed chance saved by Cech before Navas elected to square the ball rather than shooting when closing in on the Arsenal goal.
Skipper Toure gave City hope with 10 minutes remaining with a laser-guided left-footed effort that found the top corner. The ball seemed to go in in slow motion, but such was the accuracy of the shot Cech was completely helpless.
Bony was next to threaten but his shot was blocked by Laurent Koscielny, before Toure’s effort rolled just wide from a slide-rule De Bruyne pass.
Arsenal weathered the late City storm, and Pellegrini’s men must pick themselves up quickly ahead of the Boxing Day clash with Sunderland at the Etihad Stadium.
