Two-goal Shaun Wright-Phillips, Salomon Kalou and Didier Drogba did the damage to leave Sir Alex Ferguson still looking anxiously over his shoulder with just five hurdles remaining in the title race.
With his tiring troops in need of reinforcements for the final push of the season, Mourinho made five changes as the fresh-legged Wright-Phillips, Kalou, Wayne Bridge, John Obi Mikel and Lassana Diarra each received the call to arms in a game that ex-Hammer Frank Lampard had predicted would be a 'war'.
Certainly, for a side five points adrift of safety, the Hammers showed little terror or trepidation in a feisty opening that saw Yossi Benayoun's teasing cross tantalisingly clear Bobby Zamora's head, while James Collins headed over and the clever Carlos Tevez forced Petr Cech to palm away his awkward, angled chip.
There were early bookings, too, for Nigel Reo-Coker and Lucas Neill, who felled Bridge and Wright-Phillips in quick succession, while Diarra was also cautioned for hauling down the teasing and tormenting Tevez.
Following their catastrophic three-goal defeat at fellow strugglers Sheffield United on Saturday, Alan Curbishley had made a trio of switches as Jonathan Spector, Luis Boa Morte and Benayoun earned recalls in yet another must-win match for the East Enders.
And the game plan looked to be working, for apart from seeing the breaking Drogba smothered by Robert Green, the Blues had offered little attacking threat in the opening half hour.
But on 31 minutes, Mourinho's men drew first blood when Wright-Phillips collected Kalou's chest down and, after riding unconvincing challenges from Benayoun and then Spector, he curled a low, angled 18-yarder across the face of the diving Green into the bottom right-hand corner.
Down but not out, West Ham did not take long to conjure up an equaliser as Tevez whipped in an unstoppable shot from the left-hand edge of the area that curled around Michael Essien, over the ducking Paulo Ferreira and through the scorched palms of Cech to fill an ecstatic Upton Park with hope.
But sadly for West Ham that was the closest they would come to salvaging anything from the game.
Indeed, the Blues' response was instant. Straight from the kick-off, and without a single Hammer touching the ball, a slick passing move climaxed with the overlapping Bridge crossing to the edge of the six-yard box, where Wright-Phillips got in front of Neill to send his shot rocketing into the roof of the net.
Benayoun, Boa Morte and Zamora each squandered excellent chances to level either side of the break and those misses proved so costly as Chelsea romped towards the final whistle.
On 51 minutes, Lampard's free-kick caused havoc in the six-yard box where Kalou tapped the ball over the line after Green had parried Drogba's point-blank shot.
And not to be outdone, Drogba, who had been booked for infuriating the Hammers fans for his celebration of Kalou's goal, then enraged the locals even more when he raced on to Lampard's chip and took advantage of the luckless Neill's slip to slot the fourth past the exposed Green and leave his side home and hosed with half an hour still remaining.