Bobby Zamora's spectacular early strike kept West Ham's hopes of Premiership survival alive and dented Everton's push for a Uefa Cup place.
West Ham players mob Bobby Zamora after his opener against Everton
Zamora curled home a left-foot finish from 20 yards after 13 minutes to give West Ham a deserved three points.
Everton lost top scorer Andrew Johnson with an ankle injury early on, and Mikel Arteta missed their best chance of an equaliser with nine minutes left.
Yossi Benayoun was just off target for West Ham, but they held on to win.
Everton suffered a blow inside seven minutes when top scorer Johnson limped off after injuring an ankle in an innocuous challenge with West Ham captain Nigel Reo-Coker.
James McFadden came on as replacement, but Everton's fortunes failed to improve as they went a goal down in the 13th minute.
Zamora picked up the ball on the right flank and cut in to unleash a curling left-foot finish that flew high past motionless Everton keeper Tim Howard.
Everton boss David Moyes gave the struggling James Beattie another opportunity, despite the striker being without a goal in open play this season.
It was easy to see why as he bungled two of Everton's best opening of the first half.
Lee Carsley's shot rebounded into his path off James Collins, but Beattie was too slow to take advantage and West Ham cleared.
He then turned inside the area, but was unable to beat West Ham keeper Robert Green to the loose ball.
Zamora had a glorious chance to double West Ham's lead seconds after the break after a fine run by Reo-Coker, but his effort was high and wide.
Everton had made little attacking impact, but Mikel Arteta broke the shackles midway through the second half to shoot just wide.
Benayoun was inches away from doubling West Ham's lead with 16 minutes left, turning inside the area but shooting agonisingly wide.
Arteta then wasted Everton's best chance of the game after 81 minutes when Joleon Lescott nodded Tony Hibbert's cross into his path, but the Spaniard shot over from only eight yards.
West Ham manager Alan Curbishley:
"Once again we have beaten a top six side, but now we have got to go to Wigan next week and get a result against one of the teams around us.
"We have not done enough against the teams around us and we have to turn that around.
"I'm delighted with the performance but I felt we could have had more goals. We led from early on and kept a clean sheet, so I'm delighted."
Everton manager David Moyes:
"It's our first loss in eight games so we need to keep things in perspective.
"I'm not disappointed with the performance, although patches of the first-half could have been better.
"It was a blow to lose Andy Johnson early on because he stretches defences, but I thought James Beattie played well. I thought he worked hard and won some important headers.
"I think we were progressive and anyone who saw the game would say that Everton were unfortunate to come away with nothing."
West Ham: Green, Neill, Collins, Ferdinand, McCartney, Benayoun, Reo-Coker, Noble, Etherington (Boa Morte 74), Zamora (Cole 71), Tevez.
Subs Not Used: Mullins, Spector, Davenport.
Booked: McCartney, Benayoun.
Goals: Zamora 13.
Everton: Howard, Hibbert, Yobo, Stubbs, Lescott, Arteta, Neville (Fernandes 65), Carsley, Osman, Johnson (McFadden 7), Beattie.
Subs Not Used: Wright, Naysmith, Anderson.
Ref: M Clattenburg (Co Durham).