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The Hammers made it back-to-back league wins for the first time in more than a year to stay on course to complete a great escape from relegation.
Demba Ba was gifted his fourth goal in just five appearances after a calamitous Stoke mix-up, the recalled Manuel da Costa made it 2-0 and Thomas Hitzlsperger smashed in a late third to inflict a club record sixth straight away league defeat on the visitors.
Today's game was the first of back-to-back meetings between the two sides, who were also set to clash for the fourth time this season in the FA Cup quarter-finals a week tomorrow.
The Hammers had come out flying against Liverpool last week and looked set to do the same today when the recalled Carlton Cole - playing in a three-man attack - mis-hit a left-foot volley wide.
But Stoke soon began to take charge and could easily have gone ahead when Robert Green tipped over Jon Walters' flicked finish from Rory Delap's low cross.
The Hammers' three-man attack was making almost no impact but Stoke were the architects of their own demise in the 21st minute when Ba was gifted his latest goal.
There looked little danger when Mark Noble played the ball through but Asmir Begovic and Marc Wilson got in each other's way trying to clear and Ba outmuscled the latter to bundle it into the net.
Wilson's woes were quickly compounded when he was booked for hauling down Cole, with Ba seeing a shot blocked following the resulting free-kick.
Potters captain Ryan Shawcross followed in the 29th minute for a poor tackle on Scott Parker and this time the visitors were made to pay.
Hitzlsperger curled in the left-footed free-kick and Da Costa rose unchallenged at the far post to power home a header, his second goal against Stoke this season and first in the Premier League for 11 months.
West Ham were rampant and Frederic Piquionne missed a great chance to make it 3-0 when he hit the side-netting after a shot deflected straight to him.
Danny Pugh became the third Stoke player yellow carded before Hitzlsperger unleashed a trademark volley on the stroke of half-time that was tipped over by Begovic.
A desperate Robert Huth clearance prevented Ba pouncing early in the second half and James Tomkins nodded against the outside of the post from the resulting corner.
Stoke soon threw on former Hammers winger Matthew Etherington for Jermaine Pennant.
Green produced an ugly parry from Delap's long-range drive as Stoke finally managed another shot on target, while Begovic was at full stretch to tip Cole's curler around the post at the other end.
West Ham were looking content to play on the break and their opponents tried to add more pace to their own attacks when the ineffective John Carew was replaced by Ricardo Fuller.
Stoke's defence dropped another clanger midway through the half when Shawcross' attempt to nod the ball back to Begovic was seized upon by Cole, but this time the goalkeeper recovered to save.
Jones immediately replaced Delap as Potters boss Tony Pulis played his final card and the new man soon flicked a header inches wide from fellow substitute Etherington's cross.
Jones was making an impact, feeding Walters for a 20-yard shot straight at Green, who then reacted well at the feet of the latter after the ball ricocheted to the forward.
Cole shaved the post with a left-foot strike as West Ham tried to kill off the Stoke fightback before Ba was withdrawn to a standing ovation for Gary O'Neil.
The game was over seven minutes from time when Piquionne's shot from Parker's cutback was blocked and Hitzlsperger thundered in the rebound.
Fuller went close to a consolation with a curler and Victor Obinna came on for Cole and Danny Gabbidon replaced Parker as West Ham comfortably ran down the clock.