Victory lifted Jose Mourinho's side, winners of the last two Premier League titles, back to within three points of leaders Manchester United with five matches remaining.
Wright-Phillips struck twice in a hectic five-minute spell in the first half during which Argentine Carlos Tevez also netted for the home side. Goals after the break from Salomon Kalou and compatriot Didier Drogba confirmed the vast gulf in class between the sides.
United, who defeated Sheffield United 2-0 at home on Tuesday, have 81 points with Chelsea, who welcome the leaders to Stamford Bridge on May 9, on 78.
Wright-Phillips finally opened his league account for Chelsea with two quality finishes.
His opener on 31 minutes came after a deft shrug of his shoulder took him into the penalty area before unleashing a low left foot shot which arrowed across goal and into the right-hand corner.
West Ham quickly levelled when Tevez let fly from 25 metres out with a swerving shot that Petr Cech could only help into the net but their joy was shortlived as a minute later Wright-Phillips met Wayne Bridge's cross with a crisp right-foot volley that flew in.
Chelsea took full control after the break. Kalou prodded home from virtually on the line on 52 minutes after Robert Green had parried from Didier Drogba and his fellow Ivorian added a fourth just after the hour.
Relegation is now looming large for West Ham who are five points adrift of Sheffield United who sit one place above the drop zone.
West Ham's four remaining games are at home to Everton, away to fellow strugglers Wigan Athletic and home to Bolton before ending with a trip to Old Trafford to face United.
Elsewhere, England midfielder Steven Gerrard scored twice, including one penalty, as Liverpool regained third place from Arsenal with a 2-0 win over Middlesbrough at Anfield while Blackburn Rovers overcame Watford 3-1 at Ewood Park to move the bottom side closer to the drop.
Blackburn, beaten by Chelsea in the FA Cup semi-finals on Sunday, raced into a two-goal lead with a header from Congolese Christopher Samba and a cool finish from Jason Roberts in the opening 10 minutes.
Brazilian midfielder Rinaldi got one back midway through the first half only for South African Benni McCarthy to net a third for Blackburn.