Arsene Wenger praised his players for matching Birmingham's physical challenge and keeping their cool as victory kept them in the title hunt.
Goals from Robin van Persie and Samir Nasri plus an own goal from Roger Johnson earned the Gunners a sixth away victory of the season.
It was the perfect start to 2011 for Wenger and keeps his third-placed side within two points of the two Manchester clubs, United and City.
The Birmingham-Arsenal fixture has been renowned in the past for some explosive incidents and an unpunished challenge from Lee Bowyer on Bacary Sagna could land him in trouble with the Football Association.
But Wenger was delighted that his players let their football do the talking as they completed a double over Alex McLeish's side.
Wenger said: "We were aware that we had to match Birmingham physically. We were prepared today to face the challenges, physical challenges.
"We prepared ourselves as well not to lose our game plan, to be calm and to focus on putting the ball down and playing our game.
"We had the chances in the first half, got stronger and stronger and in the second half we played an outstanding game.
"We know the importance of winning at places like Birmingham because a draw away from home is not good enough, especially when you see the results of other teams today.
"Every time you play away you think a point is a disaster because you lose ground potentially."
Regarding the challenge by Bowyer, Wenger said: "I do not want to talk too much about that because I've not seen any replays yet.
"But in any case I do not want to keep that in my mind because I feel it is more important we focus on the way we want to play football."
Wenger made eight changes to the side which drew at Wigan in midweek and reverted back to the line-up which had overcome Chelsea on Monday.
The Arsenal boss said: "When I saw the fixtures I decided that I needed to rotate.
"You can change four or five in one game, then four or five in another game.
"I decided basically to change the whole lot for one game and then come back with a new bunch of players for the third game. I am paid to make such decisions."
Birmingham boss McLeish saw his side slip into the bottom three but is refusing to panic.
He confirmed his intention to bring in new blood during the January transfer window.
McLeish said: "As far as I know relegation is not decided until May and there are a lot of points at stake.
"We have a lot of games to go still and we will start to panic if we are in this position in May.
"We will try to enhance the squad in January but we won't break the club in the transfer window."
McLeish hinted he was unhappy with some of the free-kicks given against Van Persie when it appeared little contact had been made on the Arsenal striker.
From one of them, Van Persie scored the all-important opening goal.
McLeish said: "I felt two or three of the free-kicks were in the dubious category. Does Van Persie fall down easily? We have spoken about foreign players being cleverer than us. Let's leave it like that."
McLeish felt the outcome could have been different had referee Peter Walton awarded a penalty to his side after Van Persie appeared to handle when Roger Johnson headed back across the box.
McLeish said: "How the referee never saw that, I can't understand. It was handball. It hit his arm. When you play a team like Arsenal, you need those bits of luck.
"But we also know that we have lost too many daft goals and we are not scoring enough. We have not found the potent formula in forward areas."
