Birmingham 0 - 3 Arsenal
Robin van Persie curls in Arsenal's opener from a free-kick on 13 minutes
Arsenal stayed in touch with the Premier League leaders after a win which keeps them two points adrift of Manchester United and Manchester City.
Robin van Persie gave Arsenal the lead with a deflected free-kick.
The Dutchman should have then doubled it with a chip, and was almost made to pay when Roger Johnson fired over.
But Samir Nasri scored his 13th goal of the season before fine interplay between the Frenchman and Cesc Fabregas saw Johnson skew into his own net.
Seven points out of possible nine for Arsene Wenger's team over the festive period will breathe confidence into a team which faces Manchester City on Wednesday and will be eyeing the title with added fervour as 2011 begins.
But the result against a side which other big teams have struggled against - Manchester United drew at St Andrew's on Tuesday and Chelsea lost there in November - will give the French boss a hint that his team are developing different methods of winning.
This was a sometimes bruising encounter with Fabregas and Bacary Sagna on the end of the some rough treatment from Birmingham but Arsenal weathered it convincingly, whereas West Ham's win against Wolves earlier on Saturday means that Birmingham start the year in the bottom three.
Alex McLeish's decision to stick with the side which snatched a point off Manchester United seemed justified but the Birmingham boss will need to inject goals into a team which has only registered 18 in the league all season.
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As if to highlight this fact, Arsenal's trio of Nasri, Marouane Chamakh and Theo Walcott have 21 between them and it was not long before the England winger hared past Liam Ridgewell, only to shoot wide of the near post.
Although Arsenal began to stroke the ball around with their customary confidence, perhaps expected after making eight changes to the side that drew 2-2 with Wigan, the opening goal came from a disjointed period of play.
It started when a poor touch by Johnson meant he lunged in on Fabregas and although the Birmingham player got the ball, the excessive force meant he picked up a booking.
A back-pass that Ben Foster picked up then allowed Van Persie to tee up a free-kick which he curled into the Birmingham keeper's hands, serving notice of the danger to come.
Moments later Fabregas put the Dutchman through near the edge of the area and when referee Peter Walton adjudged he had been pulled back, Van Persie took full advantage, slamming the ball into the net via a deflection off Lee Bowyer in the hosts' wall.
The home supporters saw the free-kick which led to the goal as a soft one and let Van Persie know about it when he next touched the ball, so it was with ironic cheers that they celebrated a Birmingham free-kick down the other end.
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'Outstanding' Arsenal delight Wenger
Sebastian Larsson stepped up and curled a shot over the wall from 25 yards but Lukasz Fabianski tipped his effort round the post.
Thereafter, Arsenal reaffirmed their grip on the game and when another Van Persie free-kick was almost touched in by Johan Djourou, the Gunners reduced the Birmingham supporters to near silence.
The action was never far from the lone Arsenal forward in the first half. McLeish was left screaming after a cross appeared to hit Van Persie's arm in the Arsenal penalty area, and the 27-year-old then duffed a chip from only a few yards out when he wrongly thought he was offside.
Birmingham were close to making him pay for that poor decision almost immediately but a deep free-kick was somehow put over by Johnson from six yards out.
Even though the hosts were beginning to contain Wenger's side after half-time, it was the visitors who continued to look more threatening as the game wore on.
Walcott took the long way round Ridgewell on 53 minutes and when his cross was laid back to Jack Wilshere the birthday boy could not accept the gift, volleying over.
Nasri was then denied by a fine stop by Foster when he was one on one with the England keeper, but a minute later the Frenchman proved that his mental fortitude is a growing force when he swapped passes with Fabregas, who was returning from suspension, and steered in his 13th goal of the season.
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Birmingham should have had a penalty - McLeish
It was a classy goal and soothed any anxiety Arsenal and their fans were suffering.
Cue the Arsenal supporters to belt out a chorus of songs about their leading goalscorer and many of their other players - surely a sign that the game was over as a contest.
The hosts' fate was sealed when Fabregas and Nasri again played a one-two, although it may have been a three-four they were so in tune.
It ended with Nasri laying off a beautiful pass to the Spaniard and although Foster saved his shot, the ball rebounded off Scott Dann and then Johnson and into the net.
Walcott, and substitute Andrey Arshavin, could both have made it 4-0 and the game was closed out with the Gunners oozing confidence and looking very healthy as the race to the title hots up.
Birmingham substitute Nikola Zigic, on for a lucky Bowyer after he seemed to stamp on Sagna right in front of the dugouts, mustered his side's only chance of the second half when he hit the bar from a header in stoppage time.
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'Outstanding' Arsenal delight Wenger