When Carlton Cole opened the scoring for lowly West Ham just after the break Arsenal were staring at a fourth consecutive league match without a win but Walcott struck twice and Lukas Podolski sealed the victory to lift the Gunners to 39 points.
"When you do not win for four games it's important to come back for the confidence level of your environment," manager Arsene Wenger told a news conference.
"For us we have another good game now on Sunday at Newcastle who are in full confidence as well so that will be another test. I believe we have had a difficult period just now but honestly that was mainly down to the schedule we had."
City, who have been imperious at home this season, fell behind to an early goal by Liverpool's Philippe Coutinho. Captain Vincent Kompany headed the equaliser before Alvaro Negredo grabbed the winner in first-half stoppage time.
Chelsea are third on 37 points after Eden Hazard earned an unconvincing 1-0 home victory over Swansea City.
Wayne Rooney scored his 150th league goal for Manchester United as they came from 2-0 down after 13 minutes to beat Hull City 3-2, James Chester's own goal clinching a fifth consecutive win for the champions in all competitions.
United moved up to seventh position, three points behind fifth-placed Everton whose hopes of completing 2013 without a league defeat at Goodison Park were ended by a 1-0 loss to bottom club Sunderland.
Loic Remy scored twice for sixth-placed Newcastle United in a 5-1 home win over Stoke City, who took the lead but were reduced to nine men before halftime after Glenn Whelan and Marc Wilson were sent off. Stoke manager Mark Hughes was also dismissed.
Tottenham Hotspur lost ground as they were held 1-1 at home by West Bromwich Albion in Tim Sherwood's first game in charge since being named as the permanent replacement for sacked manager Andre Villas-Boas.
It was a great afternoon for the three clubs who started the day in the bottom three with Crystal Palace moving out of the relegation zone at West Ham's expense thanks to a 1-0 win at Aston Villa.
Fulham were 2-1 winners at Norwich City and only four points separate the bottom six clubs.
Cardiff City were trounced 3-0 at home by Southampton to raise more doubts over the future of embattled manager Malky Mackay who has fallen out of favour with owner Vincent Tan.
Arsenal arrested a form slump with a vibrant performance in the London derby, although they had to do it the hard way after Wojciech Szczesny's mistake allowed Cole to open the scoring in the 46th minute at Upton Park.
West Ham missed a glorious chance to make it 2-0 and were punished when Walcott's scuffed shot made it 1-1.
The England wide man then headed Arsenal in front and Podolski, on for the injured Aaron Ramsey, marked his return from a long-standing injury to complete victory from Olivier Giroud's layoff.
Manchester City have a 100 percent home record in the league but they were given their stiffest examination at the Etihad Stadium this season.
Liverpool had an early goal unluckily disallowed when Raheem Sterling poked the ball past keeper Joe Hart and was wrongly adjudged offside.
The visitors refused to get downhearted in a pulsating end-to-end contest and took the lead in the 24th minute when a flowing move ended with Coutinho slotting the ball into an empty net after Sterling had dribbled round Hart.
City equalised seven minutes later with Kompany heading a left-wing corner past Simon Mignolet despite a vain effort by Joe Allen to hack the ball off the line.
Fingers were pointed in Mignolet's direction in first-half stoppage time when the keeper could only palm an 18-metre effort from Negredo into his own net.
It was the ninth consecutive home game in all competitions in which the Spaniard had scored.
Liverpool created two excellent chances to equalise but they were spurned by Sterling and Glen Johnson as City closed to within one point of Arsenal.
"The three points are massive for us," said Kompany. "It was the hardest game we've had so far at home this season.
"I live for these games. Today we won but they were tough opponents."
Manchester United kick-started the festive programme, eventually, after a groggy opening at Hull following the late arrival of the team bus to the KC Stadium.
Forced to battle back from 2-0 down, they did so through Chris Smalling's header, a Christmas cracker from Rooney and Chester's own goal after the break.
It was rough on former United player Chester who had shot Hull in front after four minutes, but a huge boost for the champions showed their old knack of turning around unpromising situations.
The win was tarnished by a late red card for Antonio Valencia who earned a second caution for kicking the ball away.