The Gunners fell behind to Mo Diame's solo goal despite dominating the early proceedings, but Olivier Giroud equalised before halftime.
Late second-half goals from Theo Walcott and Santi Cazorla handed the Gunners the victory against tough opposition.
Arsenal remain unbeaten away from home in the league, while West Ham lost their first home match.
Here are eight things we learned from the game.
One of Arsenal's best players on the day was certainly attacking midfielder Santi Cazorla.
The former Villarreal and Malaga playmaker was always looking to create goalscoring chances for his team mates and a succession of excellent passes came close to being assists.
In all, he set up three shooting chances for others and his disguised reverse pass to Olivier Giroud in the second half was exquisite.
Cazorla topped off the display with a brilliantly-taken third goal, shooting left-footed across the goalkeeper into the far corner.
Boom, boom, boom went the ball.
An astounding 18 percent of all West Ham's passes, almost one out of every five, were hit long.
Long, and direct towards the head of Andy Carroll for the most part. To be fair, it was rather effective at times with Carroll winning 17 of his 25 aerial duels during the game, but the fact that it was almost always their uninspiring first port of call rather than an alternative method of attacking made it brutally painful to watch.
Sam Allardyce has never been one for the purists, but West Ham's performance against Arsenal was nothing short of hit-and-hope for way too much of the game.
Olivier Giroud has drawn criticism from some quarters and comparisons to Thierry Henry in others after his slow start in terms of Premier League goalscoring.
He finally opened his account in the league by sliding home Arsenal's equaliser against West Ham after a little more than five hours of play without a goal.
The French striker looked far sharper than in previous games and might have added a late second after a great pass through by Cazorla, but Giroud failed to beat Jussi Jaaskelainen.
For the record, he has notched his first Gunners league goal one game quicker than Henry.
Anyone want to guess the caption?!
Arsenal's weakness has sometimes been that of coming up against more physical teams who let Arsenal play their good football but pack the defence and try to frustrate the Gunners—before out-muscling them elsewhere on the park to good effect.
Against West Ham United they could have capitulated in similar fashion, perhaps especially without midfielder Abou Diaby in the team, but it didn't happen that way.
Arsenal won over half of the contested ground duels in the game (57 percent won) as well as 19 tackles compared to West Ham's 11. Aerially, West Ham won more with the Gunners winning 42 percent—Andy Carroll being a big factor there—but, importantly, Arsenal were able to pick up the second balls very often.
It was a good mix of power and finesse displayed by Arsene Wenger's men.
Injuries hit hard in the game at Upton Park, with both Arsenal and West Ham seeing members of their squad lost during the 90 minutes.
Keiran Gibbs was first to depart, early in the second half, and Arsene Wenger has revealed that the left-back will be a doubt for England next week as he suffered a thigh strain.
West Ham lost right-back Guy Demel to a similar injury and fellow defender Winston Reid also suffered a problem with his back but had to continue on the pitch as the Hammers had no subs remaining.
The worst injury of the day, however, came to Ricardo Vaz Te, who suffered the disappointment and pain of a dislocated shoulder after a seemingly innocuous fall following a late challenge on goalkeeper Vito Mannone.
Going back perhaps not even one season, another one of Arsenal's perceived weaknesses was the centre back position.
Early on in this present campaign it looks as though Arsene Wenger has not only quality but also good competition and depth in that particular area of the team.
Per Mertesacker was unlucky to be left out last week after some assured performances but he returned to the team against West Ham and played very well—leaving Laurent Koscielny on the bench.
Wenger can rest assured that he need not worry about much in this zone for now—other than picking which pairing will best serve the Gunners in each match.
Arsenal completed well over 500 passes, West Ham failed to even reach the 200-passes mark.
In the final third, Arsenal's completion rate was 76 percent, while West Ham barely managed a one-in-two completion rate in the final zone, managing just 59 percent completion.
The contrast in styles of play was evident from the first whistle, as Arsenal dominated possession and the home side sat back, hit it long and quick whenever possible and tried to get midfielders forward to support lone forward Andy Carroll.
Playing wide and around the back four as often as possible, the likes of Cazorla, Lukas Podolski and Aaron Ramsey were instrumental in the patient and ceaseless attacking play for most of the game—but the real pace-setter and game controller was situated behind them, in the shape of Mikel Arteta.
The Spaniard completed another excellent 95 percent of his passes during the game, totalling an excellent 106 during the match.
Here's the big question: Can Arsenal sustain its form and challenge for the Premier League once more?
The Gunners have started fairly well, winning three of their matches and only losing one. Though not comparable with Chelsea's start, the Gunners have had a harder run of fixtures and are looking very solid at present, coping with a range of opponents' styles and levels of ability.
Moving closer to Christmas, if they are in and around the top four again and not too far off the top, people will certainly be looking at them to see how their new year form goes.
It will be a while until we can assess just how far Arsenal might go this year, but their form is certainly indicative of being up there with the top teams again. Until they end that long trophyless streak though, question marks will continue to surround them as a club.
Statistics from eplindex.com