Mohamed Diame had Upton Park rocking as his stunning finish gave the hosts the lead with 21 minutes played.
But the Gunners’ slick passing meant they were always a threat and so it proved as Olivier Giroud bagged his first league goal to level things up before half time.
Kevin Nolan wasted a few chances for Sam Allardyce’s men in the second half before supersub Walcott raced through to put Arsenal in front.
Cazorla sealed the win with a fizzing effort seven minutes from time as Arsene Wenger’s men left with all three points.
Walcott said: “(Cazorla) has come in to the Premier League and taken it by storm — he’s our conductor.
“His goal was fantastic — I don’t even know what-footed he is, to be honest!”
Wenger added: “It was an outstanding performance. If you love football, just watch him play — it’s a delight to watch him.”Giroud said: “I’m so happy to score my first goal and assist my friends in the team.
“Everyone was talking about this goal, saying ’don’t worry, we trust you, keep going, concentrate’. I stayed confident.”
Arsenal left-back Kieran Gibbs, though, limped off in the second half, which could be a concern for England, although West Ham striker Andy Carroll did complete the full 90 minutes on his recovery from a hamstring problem.
Before kick-off, there was a well-observed minute’s applause for former West Ham defender John Bond, who passed away recently.
West Ham looked to utilise Carroll’s presence whenever possible, but needed all the help they could get in their own penalty area as Arsenal continued to press.First, Carl Jenkinson’s cross was hacked behind and then Carroll knocked Cazorla’s fierce drive over his own crossbar.
West Ham, though, snatched the lead against the run of play in the 21st minute.
The ball was worked down the left channel and Diame cut inside Aaron Ramsey to fire an angled drive into the top corner.
The Senegal midfielder was shown a yellow card for celebrating his first Irons’ goal by running into the crowd — and was fortunate not to have then seen red after clattering into Mikel Arteta, instead just getting a final warning from referee Phil Dowd.
West Ham were now on the front foot, with Carroll’s close-range header straight at Vito Mannone.
Arsenal had a chance to equalise when Giroud just failed to connect with Per Mertesacker’s flicked header through the six-yard box.The French striker, though, did bag his Premier League goal four minutes before half-time.
After winning the ball in midfield, Giroud stabbed it out to Lukas Podolski on the left. The German darted to the byline before cutting the ball back across goal — where Giroud arrived at pace to slot home.
West Ham, though, could easily have gone back in front just before the break when Kevin Nolan knocked the ball wide from close range after a free-kick into the Arsenal penalty area.
The Irons were fired up following the restart, forcing a succession of corners.
Arsenal left-back Gibbs hobbled off in the 55th minute, replaced by Brazilian Andre Santos — an injury concern for England ahead of their World Cup qualifiers.
Matt Jarvis’ shot-on-the-turn flew over as the hosts pressed again.As the hour mark passed, Ricardo Vaz Te had to be substituted, by Matthew Taylor, after falling awkwardly on his arm after racing to a 50/50 with the Arsenal keeper.
Wenger looked to inject some fresh life into the visitors’ attack when he sent on Walcott for Gervinho.
Walcott almost helped set up a goal when Cazorla’s shot hit Ramsey and bobble in West Ham penalty area, his clever backheel was cut into the sidenetting by Giroud from a very tight angle.
The game was wide open now as both sides created chances, Cazorla firing off target after a jinking run before Mertesacker’s last-gap tackle denied Nolan.At the other end, Podolski’s low drive was spilled behind by Jaaskelainen.
Arsenal broke away to take the lead with 13 minutes remaining.
Giroud fed Walcott, who timed his run to beat the offside trap, dart into the penalty area and beat the keeper with a low shot into the near post.
West Ham quickly spurned a chance to draw level when Nolan blasted over from 10 yards.
With 11 minutes left, Diame was replaced by Carlton Cole.
However, it was game over when, in the 83rd minute, the excellent Cazorla finally got his goal — lashing a sublime left-foot effort into the top-right corner from 25 yards.