Arsenal briefly rallied with a superb second from Walcott, but David Silva restored the two-goal lead from close range and Fernandinho poked home his second to maintain City's 100 percent home league record.
Even Per Mertesacker's late consolation for Arsenal was trumped by City as Yaya Toure stroked in a stoppage time penalty.
Arsenal's lead at the top of the table was reduced to three points as City jumped to second, three points behind.
Chelsea, who dropped to fourth, host Crystal Palace later on Saturday when victory would leave them two points behind Arsenal. Third-placed Liverpool, also five points behind Arsenal, visit sixth-placed Tottenham Hotspur on Sunday.