Their performance against a Wimbledon side still intent on earning a Uefa Cup place involved real verve and self-belief, characterised by the way their Australian substitute, Stan Lazaridis, earned them a point with a last-minute shot from outside the penalty area.
Good fortune, too, played a part - 12 minutes from time Vinnie Jones wasted the opportunity to double Wimbledon's lead when he drove over the bar from the penalty spot.
But West Ham, building on a run which had brought them seven points from the previous 12, earned their luck, and this may yet prove to be the turning point for them in their quest to avoid relegation.
Lazaridis's first goal of the season - driven home through a crowded box after a corner from West Ham's other inspirational substitute, Hugo Porfirio, had been headed away - means that four teams now stand below the Londoners in the Premiership table.
They will travel as much in expectation as hope on Saturday to face Coventry, whom they overtook yesterday on goal difference. "It's going to be a scrap until the end," said West Ham's manager, Harry Redknapp. "But it's in our hands now. We are playing well. We are not playing like a relegation team."
As Redknapp readily acknowledged, the recent signing of his forward partners, Paul Kitson and John Hartson, has made the difference. "We have had three months when no one could have got results with the team," he said. "I didn't think we were going to score a goal, and neither did the players. But we look a different team now."
Wimbledon, playing their 10th game in the space of 32 days, could have been forgiven some weariness, especially after last week's traumatic exit from the Coca-Cola Cup semi-final.
But they contributed hugely to a hugely entertaining game. Their goal after 20 minutes - a far-post header from their 38-year-old forward Mick Harford after Jones's long throw had been flicked on by Robbie Earle - came against the run of play. However, like West Ham, they created a stream of subsequent chances - "enough to win four matches," according to their manager, Joe Kinnear.
The best fell to Oyvind Leonhardsen, who saw his point-blank drive blocked by Ludek Miklosko and headed the rebound against the bar.
The penalty - given for a foul on Marcus Gayle by Tim Breacker - was Wimbledon's first since their game at Chelsea 18 months ago. They missed that one as well. Despite Jones's faux pas, it seemed as if they had done enough to take three points. But West Ham, for whom 18-year-old Rio Ferdinand, playing out of position in midfield, gave another highly promising display, maintained their endeavours and were duly rewarded.
Wimbledon (3-5-2): Sullivan; Perry, Blackwell, Kimble; Cunningham, Earle, Jones, Ekoku (Holdsworth, 84), Leonhardsen; Harford, Gayle. Substitutes not used: McAllister, Clarke Sear, Heald (gk).
West Ham United (3-5-2): Miklosko; Rieper, Bilic, Potts (Porfirio, 54); Breacker, Ferdinand, Moncur, Bishop (Lazaridis, 78), Dicks; Kitson, Hartson. Substitutes not used: Rowland, Dowie, Sealey (gk).
Referee: J Winter (Stockton).