Walcott curled home a beauty in the 33rd minute before Mesut Ozil teed up Olivier Giroud to score his 12th goal in 14 games in first-half stoppage time, with Yaya Toure`s classy reply coming too late for City.
Victory took Arsene Wenger`s side to within two points of Leicester, leaving City four points further back in third place after a third defeat in five league games and fifth of the campaign in total.
Though Alexis Sanchez missed out again for Arsenal due to a hamstring injury, there was much to celebrate for the home side, including the impressive Ozil taking his tally of assists for the season to 15.
But it was a bleak evening for City manager Manuel Pellegrini, who once again saw centre-backs Eliaquim Mangala and Nicolas Otamendi struggle in the absence of injured captain Vincent Kompany.
Mindful of the danger of allowing Ozil room to roam between the lines, City lined up in a 4-4-1-1 formation with Fabian Delph and Kevin De Bruyne on either flank and David Silva supporting the fit-again Sergio Aguero.
Reprising their tactics from January`s 2-0 breakthrough win at the Etihad Stadium, Arsenal sat back, and De Bruyne drew a save from Cech after cutting in from the right flank and letting fly with his left foot.
De Bruyne accidentally kicked the corner flag as he went to take the resulting corner and he had egg on his face again moments later when he shot narrowly wide after Aguero`s pass had put him clean through.
It was a huge opportunity and barely a minute later Arsenal were ahead.Ozil`s pass found Walcott, stationed out on the left, and he moved inside onto his right foot before whipping a glorious, crisp shot inside Joe Hart`s left-hand post from 20 yards.
Arsenal`s tails were up and right on half-time they twisted the knife, Ozil — him again — releasing Giroud to run through and drill a low shot between Hart`s legs.
Pellegrini sent on Raheem Sterling for Delph at the break, but despite an improvement in City`s play, Aguero sending a couple of tame efforts at Cech, they remained alarmingly porous at the back.
Joel Campbell spurned two chances to put Arsenal further ahead, first skying over from Nacho Monreal`s cross and then seeing a toed effort blocked by Hart after running onto Laurent Koscielny`s 60-yard pass.
Hart came to the rescue again shortly after, racing out and saving with his face after first-time passes from Ozil and Campbell presented Aaron Ramsey with a shooting chance.
Aguero, who had looked off the pace on his return from a heel injury, departed in the 63rd minute, with Wilfried Bony coming on.
Toure reduced the arrears eight minutes from time with a goal of breathtaking nonchalance, ambling onto Bacary Sagna`s pass and placing a left-foot shot into the left-hand corner as easily as if he was picking up a pen.
But despite frayed nerves among the home fans there was to be no equaliser, Bony seeing a shot deflected behind and Toure, suddenly energised, toeing the ball wide after a one-two with De Bruyne.