The priceless victory leaves the Hammers just three points from safety with a trio of gigantic games to go against Wigan Athletic, Bolton Wanderers and Manchester United.
Unbeaten in their last seven Premiership starts, fifth-placed Everton were unchanged following Sunday's last-gasp victory over struggling Charlton Athletic, which had given the Hammers a glimmer of hope until they came unstuck against quadruple chasing Chelsea on Wednesday evening.
Following the devastating 4-1 defeat to the Blues, Alan Curbishley had called for nine points from his side's four remaining games as he also made two switches, recalling Anton Ferdinand and Matthew Etherington in place of Jonathan Spector and Luis Boa Morte.
Setting about getting the first three points of a 38-point target that still by no means guarantees safety, the Hammers boss also gave a statement of intent by naming a quintet of outfield players on the West Ham United bench for the first time since the five-substitute rule came into force in August 1995.
Certainly, the East Enders had the better of the opening exchanges as Carlos Tevez and Yossi Benayoun jousted with the Merseysiders' defence and the retirement of an injured Andy Johnson with an ankle problem tipped the odds in their favour too.
And, on 13 minutes, it was no surprise when West Ham opened the scoring in spectacular style.
Benayoun invited Zamora to stroll on to his neat back-heel and the Hammers' top scorer duly claimed his 11th goal of the season by unleashing a curling 20-yarder that whipped around Alan Stubbs and under the static Tim Howard's right-hand angle.
In reply, James Beattie was denied in the act of shooting by James Collins' brilliant block and Leon Osman chested wide but, having netted once, Curbishley's strugglers were hungrily hunting a second.
Encouraged by the locals to shoot, the outstanding Lucas Neill was only an inch or so wide with a scorching 25-yarder, while Nigel Reo-Coker's deflected shot looped just over.
Neill, again, then had a header charged down by a defender to leave the visitors gratefully trooping off at the interval with only a single-goal deficit.
Having been outplayed in the first half, Everton showed far more energy and endeavour following the restart and, after piling on the pressure and giving the home defence some nervy moments, Mikel Arteta then sent a low, 18-yarder flashing past the base of Robert Green's right-hand post midway through the half.
And, with nine minutes left, the Spaniard looked all set to salvage a point when the impressive Joleon Lescott nodded the ball down into the six-yard box.
Thankfully for the desperate Hammers, Arteta's shooting boots deserted him and, with the ball flying high into the stand, Curbishley's men hung onto three points and that precious Premiership lifeline.