West Ham owed a lot to their goalkeeper Robert Green and the frame of the goal for 'keeping Arsenal out.
West Ham's goal and win goal was distinctly against the run of play, but came after Kolo Toure allowed Zamora too much space to run on to a ball over the top to then lob Jens Lehmann.
The Gunners had begun brightly and should have been 3-0 up within the first eight minutes. Cesc Fabregas, with the odds in his favour having been put through on goal by a clever Tomas Rosicky pass saw his shot parried by Robert Green after two minutes.
Within two minutes of that effort Emmanuel Adebayor shook off his markers to burst in to the left side of the area but directed his shot too close to the keeper. The same player was again through three minutes later, this time in a central position but his shot sailed high over the bar.
West Ham again had their keeper to that on 11 minutes when Fredrik Ljungberg sprung the visitors off-side trap and out-paced Anton Ferdinand into the Hammers' penalty area but found Green out quickly to block his route.
Arsenal were spurning one chance after the other. It was Rosicky's turn on 15 minutes. He arrived late into the box having been teed up for a shot from the edge of the area, but his effort flew high and wide of the left upright, when a goal looked the more likely outcome.
West Ham for their part were playing on the break, but seldom threatened Jens Lehman, although the German keeper had to be alive to a curling Carlos Tevez free-kick on the quarter hour.
The pace of the game settled a touch after then, but Rosicky went close on 25 minutes when a Toure free-kick was charged down and the ball fell at the feet of the Czech international. Rosicky curling shot across goal from the left edge of the area had Green scampering, but the West Ham keeper was relieved to see them ball fly just wide of the right post.
Rosicky was beginning to find his range and had it not been for Green being at his sharpest, the midfielder's fierce shot from the right on the half hour would have been a certain goal. The keeper however, threw his body in the way of the viciously swerving shot to block its path to goal.
Fabregas then tried his luck with a dipping 25-yarder that Green got back for to pluck from the air just before it crossed the line.
West Ham's first notable shot, apart from the goal, came on 37 minutes from Tevez, whose jinking run on the left side of the area took a deflection that killed it's velocity allowing Lehmann to gather with ease.
The Gunners began the second half with renewed purpose, but Green was again on hand to deny the Gunners when he made a finger-tip save from Gilberto's shot from the right side of the area just seven minutes after the re-start.
Green made the save of the game just after 55 minutes when he denied Adebayor with a header from point-blank range.
Five minutes later it was the frame of the goal that denied Fabregas having beaten Green with a 20-yard drive. Then a minute later Gilberto's header in front of goal fell just wide.
Arsene Wenger introduced Jeremie Aliadiere and Julio Baptista in the hope of boosting Arsenal's firepower. In the end, it was not enough.
With the minutes ticking away, the frame of the goal saved the Hammers again when Gilberto's shot on 85 minutes struck the right upright.
With just two minutes of regular time to play, Louis Boa Morte was through and rounded the keeper, but his shot rolled across the face of the goal.