Trouble was, the visitors had already been presented, gift-wrapped well ahead of Christmas, with four goals. They didn't need to score again and just managed to hang on to a 4-3 win that takes a little of the heat off their manager Terry Venables and increases the rising blood pressure of his former protege, Glenn Roeder.
This was a typical Jekyll and Hyde performance from the Hammers, who went from woeful to wonderful in one of the most remarkable transformations even by our inconsistent standards.
Mr Hyde turned up for the 2pm kick-off, which was 45 minutes before West Ham did. To say that some of the Hammers' defending in the first half was of park football level is an insult to amateur beer bellies up and down the country.
The game was just 12 minutes old when David James inexplicably came racing out to try and collect Christian Dailly's backheader, but was beaten to the bouncing ball by Harry Kewell who hooked in a cross that Nicky Barmby dived to head home into the unguarded net at the Bobby Moore Stand end.
Kewell and Mark Viduka caused regular panic stations in the home back four and it was a surprise that the next goal was scored by West Ham. A minute after Jermain Defoe had gone close with a blistering effort from distance, the returning Paolo Di Canio tucked away the rebound after Leeds keeper Paul Robinson could only parry Michael Carrick's well struck 25-yarder to his feet six yards out.
Di Canio might have put Hammers ahead when his close range effort was blocked by Robinson but Leeds looked more likely to score, especially from crosses. Kewell often dropped into midfield areas to gain possession before turning and running at West Ham and it was only a matter of time before he hurt a brittle Hammers defence.
They regained the lead on 28 minutes when Jason Wilcox's corner was met by Kewell, who headed into the net at the near post. Yet again, the elusive Aussie was left unattended by the struggling Tomas Repka, whose frustration led to an inevitable booking.
James redeemed himself by parrying Lee Bowyer's shot and clawing away Bakke's header but after the second effort on 41 minutes, the ball broke kindly for Kewell, who lashed it home right-footed.
West Ham, still looking for a first home win in eight games this season, had left themselves a mountain to climb - but it got worse in injury time before it got better.
Dailly, at right-back, badly underhit a back pass to James and when the keeper lost a 50-50 challenge with Viduka just outside his penalty area, the big Aussie had the last laugh on the crowd who gave him stick all afternoon by rolling the fourth goal into the empty net.
It was as much as the home fans could take and, not unreasonably, they booed the players down the tunnel as the half-time whistle sounded.
No-one was surprised to see Repka replaced at the interval by Sebastien Schemmel, whose introduction at right-back meant Dailly moving inside to partner Ian Pearce. Thankfully, though, the home defence were not tested again and it wasn't until Bowyer fired high into the Centenary Stand in stoppage time that Leeds mustered another shot. That's how much Hammers dominated a completely one-sided second half.
Roeder must be fuming, however, that his team had to concede four bad goals and hear his tongue-lashing in the dressing room before they found the passion and drive expected of any club struggling for points at the wrong end of the table.
West Ham came out for the second half like men possessed and, just four minutes later, Di Canio earned a penalty that he converted himself to cut the deficit to two goals.
Edouard Cisse replaced the injured Steve Lomas, which meant Joe Cole switching from centre to right midfield, where he had more of an impact on a day when he was not at his best.
Roared on by a supportive crowd, there was a new energy and commitment about the team in claret and blue, as Leeds clung to a lead that came under increasing threat.
Carrick, one who shone in the second half, tested Robinson with a 25-yard scorcher while Pearce went close with a header before the big central defender showed his value in the opposing penalty box again when he forced the corner that led to Hammers' third goal in the 70th minute.
Schemmel, who added dash to the right flank, had wasted a couple of poorly delivered crosses before his corner on the right found the head of Trevor Sinclair - playing with a mask protecting his fractured cheekbone - who scored at the near post.
How West Ham did not complete the fightback with an equaliser, they will never know. Cole sent over a perfect cross that Defoe should have headed into the net instead of wide of the far post, and when Defoe's far post cross was headed down by Di Canio, Robinson just got to the ball before Carrick.
The Leeds keeper had to be sharp to save low from Cole's shot on the turn and even in time added on West Ham could have snatched the equaliser their second half efforts deserved. Nigel Winterburn, whose commitment is needed on these occasions, swung over a deep cross, and Pearce rose above the Leeds back four to nod the ball just inches wide of the far post.
West Ham, inspired by the outstanding Di Canio, were brilliant in the second half but by then the damage had already been done.
Minute-by-minute:
6 - Di Canio's dangerous free-kick from the right misses out Radede and almost drops for Pearce in the six-yard box, but the presence of Lucic is enough to deny the chance.
11 - Another free-kick from Di Canio, this time a quickly taken chip that spots Sinclair's run from the left. However, the mask-wearing winger heads just over.
11 - GOAL. Leeds pounce on the break as a long kick from Robinson isn't dealt as it bounces on the edge of the Hammers' area and, as James comes flying out of his goal, Kewell nips in to lift the ball over the England keeper for Barmby to nod home into an unguarded net. West Ham United 0 Leeds United 1.
14 - With Hammers shell-shocked, Leeds almost grab a second, as Barmby's cross from the right is met by Viduka, who is somehow allowed to ghost through unmarked by Repka and Pearce, only for James to come to the rescue with a superb reflex save.
16 - Cole booked for foul on Viduka.
19 - Bakke's brave diving header from Harte's free-kick flashes just past the post.
20 - Defoe almost brings the Hammers back into it with a wicked curling shot from the edge of the area that fizzes just over the bar.
21 - GOAL! Hammers show their character to bounce back in determined style with an equalising goal. After Leeds fail to clear their lines properly, Carrick's low, skidding shot is only parried out by Robinson to the six-yard box, where Di Canio follows up in predatory fashion to slot the ball cooly past Robinson. West Ham United 1 Leeds United 1.
22 - Bakke booked for foul on Winterburn.
27 - Repka's chipped pass down the right is chased by Lomas, who does well to keep the ball in and send a low cross into the six-yard box, where Di Canio sidefoots the ball goalwards only to be denied by a fine save by Robinson.
28 - GOAL. Hammers' defensive frailties let them down once more, as Kewell escapes his marker yet again to meet Harte's near-post corner with a firm header that gives James no chance. West Ham United 1 Leeds United 2.
33 - West Ham are at sixes and sevens defensively, as Bowyer runs through unmarked and fires in an effort that James beats away. Winterburn then has a chance to clear, but is dispossessed by Barmby, who races into the area and cuts the ball back for Kewell, who thankfully scoops his shot over the bar.
38 - Repka booked for ungentlemanly conduct.
38 - Viduka booked for ungentlemanly conduct.
41 - GOAL. Hammers are given a mountain to climb as yet more poor defending gifts Leeds a third goal. After James does well to stop a Bakke header, Lomas loses out in a challenge on the edge of the box and the ball is played out wide to Harte, whose left-foot cross is diverted by Pearce on to the boot of Kewell who, unmarked once again, fires a sweet, right-footed volley past James into the bottom corner for his second of the match. West Ham United 1 Leeds United 3.
Added time: 3 minutes.
45 - Kewell runs on to Viduka's flick and is only denied his hat-trick by a smart stop from James.
45 - GOAL. It goes from bad to worse, as Dailly's weak back-pass forces James to run out and try to clear under pressure from Viduka, but the ball cannons off the Aussie, who can't believe his luck as he strolls on and passes the ball into an empty net. West Ham United 1 Leeds United 4.
Half-time: West Ham United 1 Leeds United 4.
Second Half:
46 - Substitution for West Ham, Schemmel replaces Repka.
49 - Just moments after seeing a penalty appeal waved away, Di Canio skips into the area and goes down under Kelly's challenge. Referee Dunn immediately points to the spot.
50 - GOAL! Di Canio strokes home confidently from 12 yards out. West Ham United 2 Leeds United 4.
51 - Substitution for West Ham, Cisse replaces Lomas.
52 - Di Canio booked for foul on Kelly.
60 - Schemmel booked for foul on Wilcox.
64 - Cisse sends a speculative effort flying over the bar from 30 yards out.
68 - After Di Canio's driven low cross is cleared by Radebe, Carrick chests down and fires in a scorching right-foot volley that Robinson holds well.
70 - Di Canio's flighted free-kick is met by Pearce, who heads just wide of the target at the far post.
74 - GOAL! Hammers give themselves a chance of setting up a memorable comeback, as Schemmel's near post corner from the right is met by Sinclair, who powers his header past Robinson into the roof of the net. West Ham United 3 Leeds United 4.
76 - Substitution for Leeds, Bridges replaces Viduka.
78 - Cisse, looking dominant in the centre of midfield, sees another dipping effort fly high over the bar.
80 - Cisse booked for foul on Bridges.
82 - Cole collects on the right and whips in a superb cross that appears to be dropping perfectly for Defoe. However, the young striker fails to connect properly and the ball drifts agonisingly away for a goal kick.
84 - Defoe hangs up a cross from the right that Di Canio meets at the far post and heads into the danger area, where the fist of Robinson just beats Carrick to the ball.
85 - Substitution for Leeds, Millner replaces Wilcox.
87 - Bowyer booked for foul on Di Canio.
88 - Cole's stunning turn on the right takes him away from two defenders but the final ball into the box is sadly lacking as Radebe clears.
Added time: 3 minutes.
90 - Pearce sprints forward from his centre-half position and his run is spotted by Winterburn, who floats in a hanging cross that the big defender heads just inches wide of the post.
90 - Substitution for Leeds, McPhail replaces Kewell.
Full-time: West Ham United 3 Leeds United 4.