Gerard Houllier's side certainly have their injury problems, with Robbie Fowler, Jamie Redknapp, Vladimir Smicer and Titi Camara already out, and there was the worrying sight of Michael Owen limping off late on with apparently yet more hamstring trouble.
Owen was also booked for diving in the first-half as Houllier's warnings about the theatrics of Paolo di Canio proved completely unfounded - apart from the damage that the Italian wreaked with his extravagant touches.
After going seven matches unbeaten in the FA Carling Premiership - something of a record over the past couple of seasons - Liverpool let their guard down in defence when it mattered most and were relatively toothless up front with just one central striker.
The visitors certainly had their chances to equalise in a game which eventually improved after a poor first-half but the Hammers just about deserved their victory, courtesy of Trevor Sinclair's close-range strike on the stroke of half-time.
Upton Park is therefore yet again proving to be a fortress, with Harry Redknapp's side having dropped only two points on their home ground all season.
They took some time to get into the stride, however, in a largely uneventful first-half as both sides crammed the central midfield and left little room for manoeuvre.
At that stage, the Liverpool back four - protected by a five-man midfield in which Patrik Berger was replaced by David Thompson when the Czech limped off after just 18 minutes - was in determined mood.
The visitors even had the first chance of the game just two minutes later when Sinclair, who had been involved in the challenge which led to the winger's enforced departure, played a woefully short back-pass towards keeper Shaka Hislop.
Owen was onto the ball in a flash but, as he controlled the ball and turned towards goal, Hislop intelligently retreated and was in position to save the striker's shot when it eventually came straight at him.
Owen was again at the centre of the action two minutes before the break when he dashed into the penalty area at full speed but then went flying to the ground after the slightest contact with defender Neil Ruddock.
Referee Graham Barber, who had earlier turned down a half-hearted penalty appeal for handball by the visitors, was unimpressed and promptly showed him the yellow card.
That was the cue for the Hammers to launch an assault themselves and, with just seconds of the half remaining, they finally broke the deadlock.
The industrious Steve Lomas, back from suspension along with Javier Margas, popped up on the left flank and crossed for di Canio to hit a first-time shot which previously untroubled keeper Sander Westerveld could only parry.
The ball fell to Sinclair just a couple of yards out and the winger made no mistake as he bundled it home into an unguarded net.
Liverpool displayed greater urgency after the interval and even had the ball in the net on 52 minutes - only for Owen's effort to be disallowed.
Rigobert Song overlapped down the left flank and crossed deep towards Thompson at the far post but the the ball was deemed to have crossed the byline before the midfielder managed to play it back for Owen to head into the net.
Thompson threatened again just two minutes later when he curled an effort just wide from 20 yards out and Steven Gerrard was also starting to get into the game as the Hammers were being forced to hang on.
They managed it, however, as Liverpool started to make harder work of their build-up play and the Hammers finally started to offer an attacking threat themselves - only for Wanchope to waste two openings.
First the striker hesitated before taking aim inside the penalty area and allow Henchoz slid in with a perfect sliding tackle, and then his square ball to di Canio on the break was intercepted by Sami Hyypia.
Liverpool were forced to regroup in the final 15 minutes after Owen was forced off, with defender Steve Staunton on as substitute, and certainly came close to an equaliser.
Thompson, Murphy and Gerrard all threatened yet West Ham held out, with Hislop making one important save from Thompson, and even threatened to punish Liverpool on the break.
A wonderful piece of control by Joe Cole, who came into his own in the latter stages, was followed by a pinpoint crosss which was met by a flashing header from di Canio that struck the upright.
But Wanchope was far too slow to react to the rebound and, under pressure, he ballooned his shot over from close range.
The striker, who had played poorly, was substituted soon afterwards and appeared to exchange angry words with members of the crowd on his way off the pitch.
There was still time for Cole to shoot over the bar after a remarkable run by di Canio but West Ham were home and dry and Liverpool were left to start all over again with their assault on the top three.