But Alan Pardew's eighth-placed side still remain unbeaten in nine league and cup games, while David Moyes can take heart from a battling Everton display that left his side in 12th spot.
Unbeaten since their defeat to champions-elect Chelsea on January 2, West Ham were unchanged from the team that had forced an FA Cup fifth round replay at Bolton Wanderers a fortnight earlier.
Everton, on the other hand, made three switches as Tony Hibbert, Phil Neville and James McFadden returned to a side beaten by two-goal Nolberto Solano's blast at Newcastle United last weekend.
And despite having the best of the opening exchanges, the Merseysiders found themselves trailing after just ten minutes when Nigel Reo-Coker and Dean Ashton combined to allow Yossi Benayoun to find Marlon Harewood who turned and stroked a low 15-yarder past Sander Westerveld.
The Hammers striker's 13th goal of the season had come courtesy of a fine passing movement but, within eight minutes, Everton were level thanks to an equally incisive move that saw McFadden and Mikel Arteta combine to invite Leon Osman to claim his third strike of the campaign with an unstoppable ten-yarder.
Midway through the half, however, West Ham regained the advantage with a less aesthetically pleasing route one effort that saw Harewood flick on Shaka Hislop's huge drop-kick, whereupon Ashton duly drilled a clever, tightly-angled eight-yard shot past Westerveld.
Everton's frustration grew on the half-hour mark, when Hibbert joined Neville in referee Mike Riley's notebook for tripping the fleeing Matthew Etherington and, as the interval neared, the stretching Lionel Scaloni then hooked James Beattie's bobbling effort off the line, before Alan Stubbs saw another goal-bound effort saved by Hislop.
Just after the restart, Harewood got the better of the exposed Westerveld only to hook the ball both high and wide and that was to set the tone for a scrappy second half that was to be dominated by Everton.
After Benayoun was booked for encroachment, Anton Ferdinand and Arteta then saw themselves yellow-carded for a senseless scuffle as Everton broke upfield.
And on 70 minutes, with Sven-Goran Eriksson looking on, the afternoon got yet worse for Ferdinand who saw Beattie pounce to hook his ninth goal of the season over Hislop, after he failed to deal with Nuno Valente's cross into the danger zone.
Having seen his side surrender the lead twice, Pardew then replaced his two strikers with Bobby Zamora and Teddy Sheringham but, by then, the Hammers' hopes of a sixth consecutive Premiership victory had long evaporated into the chill East End air and, indeed, only Danny Gabbidon's last-gasp diving, defensive header denied Everton victory.