A first half penalty from Santi Cazorla and a second half Olivier Giroud header secured all three points for the North London club, reigniting their Champions League ambitions whilst leaving second place Manchester City five points adrift of Chelsea.
Arsenal have had a terrible record against top four opposition away from home in recent years, and little was expected of a team ravaged by defensive injuries. Last season Manchester City won the corresponding fixture 6-3.
Instead, Arsenal put in a supremely disciplined performance against a Manchester City team without their talismanic midfielder Yaya Toure, who is now at the African Cup of Nations, and struggling to score goals.
Although striker Sergio Aguero started, he looked rusty and rarely threatened Colombia World Cup goalkeeper David Ospina in the Arsenal goal.
It took a soft penalty to open the scoring, when Manchester City's captain Vincent Kompany was judged to have impeded Nacho Monreal as he marauded into the box. Santi Cazorla, by far the best player on the pitch, dispatched the penalty despite Manchester City goalkeeper Joe Hart guessing the right way.
"The penalty changed the game," Manchester City coach Manuel Pellegrini told Sky Sports after the game, hinting that he believed Monreal deceived the referee. "It was not a penalty," he added.
Manchester City didn't look like equalizing and it wasn't a surprise when Olivier Giroud doubled the lead with a header early in the second half, converting from a Cazorla free kick.
"We played high up in their half and it worked because we knew we wanted to make the space tight and we did it well," Arsenal coach Arsene Wenger said after the game. "People are very quick to judge and you forget we have many defenders out. It was down to discipline. We have a very important fight in front of us."
The victory lifted Arsenal into fifth place, one point behind Manchester United. Manchester City, however, are now five points behind leader's Chelsea. The two meet at Stamford Bridge in a fortnight.
Meanwhile, in Sunday's other English Premier League game, West Ham United continued their brilliant start to the season by swatting aside relegation threatened Hull City.
Second half goals from Andy Carroll, Morgan Amalfitano and Stewart Downing kept up their outside shot at Champions League qualification.