Sam Allardyce's men had weathered some heavy pressure in the first period and snatched the lead early in the second through Carlton Cole - only for the Gunners to come up with a whirlwind final quarter and seal a surprisingly comfortable victory.
Also pleasing for Arsene Wenger was the successful return of Germany forward Lukas Podolski, who wrapped up the points having come off the bench, but both Aaron Ramsey and West Ham's James Collins were forced off by new injuries during the game.
It was the hosts who produced the first meaningful attempt at goal in the 10th minute - Mark Noble nearly punishing a needless Mikel Arteta foul with a free-kick that forced Wojciech Szczesny into a full-stretch save.
The Gunners were struggling to dissect a determined home defence and when they did in the 26th minute, Walcott should have done better than volley a precision lofted pass from Ramsey wide of the near post.
Santi Cazorla was two feet too high from distance on the half-hour mark and Olivier Giroud cut a frustrated figure having wasted a pair of openings created by well-timed Mesut Ozil passes. Arsenal were left ruing their misses in the very first minute of the second half.
Wojciech Szczesny will take the vast majority of blame for spilling Kevin Nolan's tame long-ranger but his defenders did him few favours, allowing Cole to pounce on the loose ball unattended and tuck home from close range.
The Pole went some way to atoning by smothering a Matt Jarvis attempt, and there were further scares for Arsenal before the hour mark - Joey O'Brien sending a free header the wrong side of the post and Cole failing to turn in a Jarvis cross.
It took a piece of poor goalkeeping to open the floodgates for Arsenal in the 68th minute. Walcott teased George McCartney onto the back foot, shifted the ball inside to shoot off his left foot and, despite making poor contact, Adrian could only usher his effort into the net.
Walcott's second, just three minutes later, was more impressive. Podolski whipped over a cross that James Tomkins could only flick on - prompting Walcott to hang in the air a little longer in order to arrow a header past Adrian.
Podolski had already fired a pair of range-finders - the second a shot from an exquisite Cazorla pass that was well-saved by Adrian - by the time he marked his return to action with a goal. Giroud was his assistant, the Frenchman holding the ball up in the area before teeing up for Podolski to blast home from 15 yards.
Another substitute, Nicklas Bendtner, was a foot away from adding insult to injury as the game drifted into injury time but the Hammers' second half was summed up neatly by Joe Cole's tame attempt to snatch a last-gasp consolation goal.