Arsenal, United enjoy Boxing Day comebacks
Manchester United's English striker Wayne Rooney (L) looks on after scoring a goal during the English Premier League football match between Hull City and Manchester United at The KC Stadium in Hull on December 26, 2013
Arsenal spurned several first-half chances at Upton Park and they were punished early in the second period when Carlton Cole put the hosts in front after Wojciech Szczesny spilled a shot from Kevin Nolan.
However, Walcott struck twice in three minutes to turn the game around, squeezing a low shot past West Ham goalkeeper Adrian in the 68th minute and then heading home a cross from substitute Lukas Podolski.
Podolski was making his first appearance since August after a hamstring injury and he marked his comeback with a goal in the 79th minute, drilling home from Olivier Giroud's lay-off.
Victory sent Arsenal three points above former leaders Liverpool, who visit fourth-place Manchester City later on Thursday, while West Ham slump to second-bottom.
Chelsea also leapfrogged Liverpool, moving up to second place by beating Swansea City 1-0 in one of the day's 10 traditional Boxing Day fixtures.
Belgian winger Eden Hazard scored the game's only goal in the 29th minute at Stamford Bridge, cutting in from the left in familiar fashion before letting fly with a low drive that squeezed beneath Gerhard Tremmel.
Everton's hopes of making further ground on the Champions League contenders were thwarted, however, as they crashed to a 1-0 defeat at home to bottom club Sunderland.
Ki Sung-yueng scored the game's only goal from the penalty spot in the 25th minute, after Everton goalkeeper Tim Howard was sent off for a foul on the South Korea international.
It was Sunderland's first away win since April and left Gus Poyet's men three points from safety.
Manchester United doggedly overturned a two-goal deficit to win 3-2 against Hull City at the KC Stadium and register their fifth consecutive win in all competitions.
Early goals from James Chester and David Meyler gave Hull a 2-0 lead, only for Chris Smalling and Wayne Rooney to bring United level before half an hour had been played.
Rooney's goal, a sumptuous volley, was his 150th for the club in the top flight and he contributed to the winner in the 66th minute by pressuring Chester, a one-time United youth player, to put through his own goal.
"To be two down and come back to win is a great result," United manager David Moyes told the BBC.
"There's a long way to go in the league and we have to keep picking up points. I believe we can be in the mix and challenge whoever is near the top."
Newcastle United closed to within two points of the Champions League places by coming from behind to overwhelm nine-man Stoke City 5-1 at St James' Park.
Stoke took the lead through Oussama Assaidi, but they had Glenn Whelan and Marc Wilson sent off, allowing Newcastle to prevail through a Loic Remy brace and goals from Yoan Gouffran, Yohan Cabaye and Papiss Cisse.
Tottenham Hotspur's new permanent head coach Tim Sherwood saw his side draw 1-1 at home to West Bromwich Albion, for whom Jonas Olsson cancelled out Christian Eriksen's 36th-minute free-kick.
Southampton, meanwhile, ended a run of six games without victory by winning 3-0 at Cardiff City through a Jay Rodriguez brace and a Rickie Lambert strike.
Scott Parker scored a stunning 87th-minute winner as Fulham won 2-1 at Norwich City, but they remain in the bottom three due to Crystal Palace's 1-0 win at Aston Villa, which lifted Tony Pulis's men out of the drop zone.