In the Premier League, there's a well known saying that states you must convert your chances when you're dominating a game.
The hosting Hammers were two points adrift of their visitors heading into the contest, but for the opening 80 minutes, they looked much the better of the two sides.
Craig Bellamy was at the heart of virtually every West Ham attack as Everton found the Welshman's pace and directness tough to nullify. Indeed, it was Bellamy that created his team's first meaningful opening for Freddie Sears, but the young striker saw his effort tipped on to the bar by Everton goalkeeper Tim Howard.
Sears missed another chance before the break and then after the restart he could have squared a pass for either Bellamy or Scott Parker to roll the ball in, yet he went for goal himself and was off target.
However, in the 63rd minute, Gianfranco Zola's men grabbed the goal that their performance up until that point had deserved. Bellamy and Parker combined to free Jack Collison inside the area and the substitute showed good composure to curl his effort inside Howard's far post.
West Ham had not kept a clean sheet in the Premier League up until this encounter and despite all of their control, the wait for a shut out would be extended when the Merseysiders drew themselves level with seven minutes left to play. Louis Saha crossed from the right for an unmarked Joleon Lescott, who punished the space that he was afforded by sending his downward header beyond a helpless Robert Green.
Then, just two minutes later the home side hit the self destruct button. This time Saha turned scorer when his scuffed shot from a low Victor Anichebe cross squirmed into the net via a deflection and the post. If that wasn't bad enough for West Ham, it got even worse within the next 120 seconds.
Full-back Julien Faubert's pass was intercepted by Tim Cahill, with the Aussie in turn playing in Saha. With 20 yards between himself and the goal, the Frenchman sent a dipping right-footed shot that got the better of Green.
Speaking after the final whistle, victorious boss David Moyes said: "I thought it was going to be one of those days. Did I expect that finish? Probably not. But Louis Saha came up with the goods. You'll hear me talk a lot of the result at the moment. That'll do, the performances will follow."
As for Zola, he added: "It's very difficult to accept. It is not the first time we've spoiled a good job in the last 10 minutes of a game. It is something that concerns me very much, obviously. The only thing I can say right now is that we need to find a solution. Maybe I have to give something more because the Premier League is punishing. You cannot afford to drop your attention for a minute."
West Ham: Green; Neill, Collins, Upson (Collison), Ilunga, Faubert; Parker (Di Michele), Bowyer, Bellamy, Boa Morte (Etherington); Sears
Everton: Howard; Neville, Yobo, Jagielka, Lescott; Arteta, Cahill, Rodwell (Vaughan), Osman; Saha (Hibbert), Anichebe (Baines)