West Ham's top-four hopes suffered a blow after they were beaten 4-1 by Swansea on Saturday in the penultimate game to be played at Upton Park.
A victory for the Hammers would have taken them within two points of fourth-placed Manchester City, but a rampant Swansea sprung a shock through goals from Wayne Routledge (25), Andre Ayew (31), Ki Sung-yueng (51) and Bafetimbi Gomis (90+3) .
Stephen Kingsley's own-goal (68) had briefly reduced the deficit for West Ham, who remain in sixth place after suffering their first home defeat since the end of August.
Swansea move up two places to 11th after claiming their first victory in east London for 60 years.
West Ham will play their final match at Upton Park on Tuesday night when they take on Manchester United, live on Sky Sports 1 HD.
Slaven Bilic made two changes to the West Ham team that won 3-0 at West Brom last Saturday, with Darren Randolph and Victor Moses coming in for Adrian and Diafra Sakho, and he was initially rewarded with a positive start.
Dimitri Payet came close to opening the scoring inside three minutes, but his curling effort from the edge of the box was turned behind by Lukasz Fabianski.
The France international continued to be a threat for West Ham and went close again after 18 minutes, firing a free-kick just over the crossbar.
But, against the run of play, Swansea broke the deadlock and stunned a boisterous home support into silence. Ki and Kyle Naughton combined to great effect with the latter delivering a fabulous first-time ball across the six-yard box for Routledge to tap home.
From then on, Swansea grew in confidence and were soon 2-0 up. Kingsley, one of six changes made by Francesco Guidolin, picked out Ayew inside the 18-yard box and the forward made no mistake, crashing his effort past Randolph.
West Ham briefly threatened to pull a goal back before half-time, but Andy Carroll and Manuel Lanzini failed to keep their efforts on target.
After the interval, Swansea continued to be the most threatening of the sides and grabbed their third when Ki rattled his volley into the bottom corner of the net following good work on the left flank by the impressive Modou Barrow.
Kingsley raised hopes of a West Ham comeback when he inadvertently bundled home from close range after Michail Antonio and Sakho were denied by Fabianski.
But Swansea would extend their lead in the closing stages with substitute Gomis slotting his shot into the bottom corner after a neat exchange of passes with Ayew.
Soccer Saturday verdict - Paul Merson
I thought Swansea were outstanding, I really did. They picked their passes on the counter attack and they were very ruthless.
The atmosphere at the start of the game was absolutely phenomenal, at the end you would have thought it was raining. It was terrible. The fans couldn't believe it, Bilic couldn't believe it.
Everybody has one of those games in their locker during the season, I don't care who you are. But to pick this day, and I really do think it was 'Oh, Swansea have got six changes, we'll turn these over'
Match ratings
West Ham: Randolph (6), Antonio (5), Cresswell (5), Reid (5), Ogbonna (5), Noble (6), Kouyate (5), Moses (5), Lanzini (6), Payet (6), Carroll (5).
Subs used: Valencia (N/A), Sakho (6), Emenike (5).
Swansea: Fabianski (7), Naughton (7), Fernandez (7), Amat (7), Kingsley (7), Ki (8), Cork (7), Fer (7), Routledge (7), Barrow (8), Ayew (8).
Subs used: Rangel (7), Britton (N/A), Gomis (7).
Man of the match: Andre Ayew.