Late goals from Angelo Ogbonna and Michail Antonio put West Ham on the verge of a place in next season's Europa League as the visitors came from behind to beat West Brom 3-1.
A win puts the Hammers on the brink of Europe's second most prestigious club competition next season as they go three points clear of seventh-placed Tottenham heading into the final day.
West Ham host Southampton on Sunday knowing a point will secure them a Europa League place.
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West Ham were awarded a penalty in the first minute by referee Michael Oliver after Antonio was carelessly wiped out by goalkeeper Sam Johnstone, but captain Declan Rice ensured his wait for a Premier League away goal continued as he smashed his spot-kick off the post to the delight of the 5,247 fans in attendance at the Hawthorns. It was the earliest missed penalty (2') in Premier League history.
West Brom responded brightly and caused West Ham issues down the flanks. The visitors took the lead in the 26th minute when Matheus Pereira's seemingly goalbound cross from a corner was flicked over stand-in goalkeeper Darren Randolph by Tomas Soucek into the net.
The Hammers grew back into the game and Soucek scored at the right end in first-half injury time, tapping in a squared Said Benrahma pass from point-blank range which stood after a lengthy VAR review pondered whether the Czech Republic international was offside.
Semi Ajayi surprisingly had the best chance to give West Brom the lead again in the 57th minute, but his stabbed effort from point-blank range after a long throw was smartly blocked by Randolph.
Aaron Cresswell struck the woodwork after catching Johnstone well out of position from a free-kick seven minutes later, but West Ham did find their winner late on.
In the 82nd minute, Pablo Fornals off-balance forced the West Brom goalkeeper into using his toe to clear behind for a corner when Ogbonna nodded in unmarked to give West Ham the decisive lead.
With West Brom leaving gaps at the back in search of an equaliser, West Ham countered and Antonio wrapped up all three points two minutes from full-time as he coolly slotted his finish past Johnstone.
TALKING POINT - West Ham did what was necessary
It's a valuable victory for West Ham, who had to battle hard to beat a West Brom side who attacked right until the very end as they looked to put on a show for the boisterous crowd inside the Hawthorns.
West Brom looked the more likely to score at times in the second half with the game finely poised at 1-1, but West Ham always carried a threat on the break with Ogbonna and Antonio doing what was necessary in the end.
The Hammers look set for Europe and their performances have deserved it this season.
MAN OF THE MATCH - Matheus Pereira
He may have been on the losing side but the Brazilian was a constant threat down the right flank and his crosses into the box regularly caused the West Ham defence problems.
With 10 goals and seven assists in the Premier League this season from midfield for a relegated club, Pereira will surely be signed by a top-half side in England's top flight this summer. His performance on Wednesday night was a timely reminder for onlooking clubs of his ability to combine flair with output.
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West Brom: Johnstone (6), Furlong (5), Bartley (6), Ajayi (6), Townsend (5), Yokuslu (6), Maitland-Niles (6), Gallagher (5), Pereira (8), Robson-Kanu (5), Phillips (5). Subs: Diangana (6), Grant (N/A), Diagne (N/A)
West Ham: Randolph (7), Coufal (6), Dawson (6), Ogbonna (6), Cresswell (7), Soucek (6), Rice (4), Fornals (6), Lingard (6), Benrahma (6), Antonio (7). Subs: Bowen (6), Diop (N/A)
1' - PENALTY TO WEST HAM! Antonio goes down in the box after colliding with Johnstone and referee Michael Oliver points to the spot! Johnstone is booked for clattering into the striker and West Ham have a golden chance to go 1-0 up in the opening few minutes! Captain Declan Rice will take it...
3' - MISSED PEN! Rice smashes his penalty off Johnstone's right post! Rice is still yet to score a goal away from home for the Hammers and that was a poor miss! A huge opportunity has been squandered!
26' - GOAL!!! Pereira's powerful cross from the corner goes straight into the net!!! His cross comes off the top of Soucek's head and gets the better of Randolph! West Brom lead!
45+1' - GOAL? Right on the stroke of half-time West Ham level and it's Soucek who stabs in from point-blank range! Benrahma's squared pass finds the Czech midfielder and he taps in... but was he offside? VAR is checking it. GOAL!! It stands!
57' - BIG CHANCE! Ajayi stabs a shot on goal from point-blank range but it's straight at Randolph and West Ham can clear!
82' - GOAL!!! From a West Ham corner, the ball swung is met by Ogbonna and he nods into the net from close range!
88' - GOAL!! Antonio has sealed all three points for West Ham! With the Baggies leaving only two men back, the Hammers break forward through Fornals before he lays it off to Lingard and then Antonio who slots it into the bottom corner.
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