Alessandro Diamanti saw a spot kick saved as West Ham blew the chance to pick up at least a point at the Emirates Stadium this evening.
Having gone behind early on through Denilson, the Hammers had the perfect chance to level just before the interval when Thomas Vermaelen was sent off for bringing down Guillermo Franco.
But he could not beat Manuel Almunia and the Gunners held on with ten men in the second half, even adding a second late on via a Cesc Fabregas penalty.
The result keeps Arsene Wenger's troops on course for the title, while West Ham remain firmly in the relegation mix.
It took Arsenal just five minutes to take the lead. Denilson played a neat one-two with Nicklas Bendtner on the edge of the box, before hitting a crisp drive low into the corner, keeper Robert Green beaten by the pace and precision of the shot.
The goal not surprisingly settled the hosts down and Bendtner was narrowly wide with another long-range effort just a few minutes later.
However, the Hammers almost found an early way back into the game, Diamanti just over the bar with a curling free-kick.
And Mido almost got on the end of a Junior Stanislas centre, as the Hammers responded well to their early set-back.
Emmanuel Eboue dragged a shot wide for the home side on 20 minutes, but the visitors had successfully steadied the ship and prevented the Gunners from having it all their own way.
Arsenal continued to look the more threatening, but chances were now in short supply, a few balls across the face of the six-yard box the greatest threat they could pose in the remainder of the first half.
And, with a minute of the first period to go, Vermaelen was judged, perhaps harshly, to have brought down Franco as he raced towards goal.
The referee, though a long way from play, pointed straight to the spot and handed Vermaelen a red card.
However, the Hammers were unable to go in at the break on level terms, Diamanti's penalty superbly saved by Almunia.
West Ham, not surprisingly, saw even more of the ball in the second half and it made for an intriguing contest.
With an hour gone, Fabregas was a couple of feet wide with a free-kick for Arsenal, the Gunners themselves still looking capable of adding a second.
For all of their nice football, the Hammers lacked a cutting edge in attack, often guilty of not pulling the trigger when in a useful position.
Diamanti did see a shot deflect wide midway through the half, the visitors' sense of urgency ever increasing.
With 12 minutes to go, West Ham sub Carlton Cole made room for himself and fired low. His shot beat Almunia, but clipped the outside of the post.
Apart from the penalty, it was the Hammers' best chance.
And, just a few minutes later, Matthew Upson handled as Fabregas tried to get past him just inside the box.
Fabregas stepped up to the spot and sent Green the wrong way with the perfect penalty, achieving what Diamanti had failed to do.
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