Jesse Lingard continued his stunning form with West Ham by scoring twice in the first half to set the Hammers on course for a crucial victory over fellow Champions League hopefuls Leicester City.
The two sides came into the weekend occupying the last two Champions League spots, before wins for Chelsea and Liverpool on Saturday nudged West Ham down to sixth place.
But David Moyes' men showed they are up for the challenge of qualifying for Europe's top club competition for the first time, going 3-0 up and holding on during a late Leicester rally to climb back into fourth.
The Hammers took the lead as Arthur Masuaku's cross went through to right-back Vladimir Coufal, who cut back for Lingard to sweep the ball inside Kasper Schmeichel's near post from the edge of the box.
Jarrod Bowen then beat the offside trap to race on to Issa Diop's long ball and square for Lingard to tap into an empty net for his eighth goal in nine Premier League games since arriving on loan from Manchester United.
The 28-year-old forward, whose recent form earned him an England recall, then played a part in West Ham's third goal right after half-time as Bowen poked in from Tomas Soucek's pass to round off a clinical team move.
Kelechi Iheanacho pulled a goal back to give the visitors hope, before grabbing his 11th goal in 11 games in stoppage time, but the Hammers ensured they did not surrender a 3-0 lead for the second straight home game and move within a point of third-placed Leicester.