Burnley's hopes of European qualification were boosted by completing the double over West Ham with a 1-0 win which owed plenty to some fine goalkeeping from Nick Pope at the London Stadium.
Golden glove-chasing Pope racked up his 14th clean sheet of the season with stunning stops from Tomas Soucek, Michail Antonio and sub Sebastien Haller either side of Jay Rodriguez's strike (38) as Burnley continued their excellent run of form.
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The visitors' third 1-0 win in four games moves them up to ninth in the Premier League table, while David Moyes' West Ham will be ruing those missed opportunities after a defeat which leaves them four points above the relegation zone with four games remaining.
West Ham: Fabianski (7), Cresswell (6), Fredericks (5), Ogbonna (6), Diop (6), Soucek (7), Rice (6), Bowen (7), Fornals (6), Yarmolenko (6), Antonio (6).
Subs: Haller (5), Ajeti (n/a)
Burnley: Pope (9), Taylor (7), Bardsley (7), Long (6), Tarkowski (7), Pieters (6), Brownhill (6), Westwood (6), McNeil (7), Rodriguez (7), Vydra (7).
Subs: Wood (7)
Man of the match: Nick Pope (Burnley)
How Burnley won at West Ham…
Injury-hit Burnley should have been ahead with just eight minutes on the clock when Matej Vydra teed up Erik Pieters but the Dutchman blasted wastefully over the bar before Vydra headed straight at Lukasz Fabianski.
But it was the goalkeeper at the other end who was worked harder early on, with Pope forced into two stunning saves inside two minutes, first blocking Soucek's close-range volley before kicking away Antonio's drive.
Andriy Yarmolenko made his first start since November for West Ham. The Ukrainian winger, who scored the winner against Chelsea seven days ago, replaced Manuel Lanzini in the only change for the hosts.
Burnley were unchanged from the side which drew with Sheffield United.
Those interventions from Pope - who is now ahead of Liverpool's Alisson in the clean-sheet standings - paid off on 38 minutes when Rodriguez met Charlie Taylor's cross from the left and, with his head and shoulder, directed the ball in off the underside of the bar and a despairing Fabianski to put Burnley ahead.
West Ham will have felt aggrieved to go behind after having the better of the chances and should have levelled immediately when a deflection put Antonio through on goal and he steered his shot onto the outside of the post.
With the game opening up before the break, Vydra mis-kicked Pieters' chipped through ball before Andriy Yarmolenko's low strike for the hosts was parried out for a corner by Pope.
After the break, Burnley centre-back James Tarkowski appeared fortunate to only receive a yellow for a high challenge on Jarrod Bowen and the defender blocked a shot from the West Ham man soon after, following a stunning save from Pope to deny Haller what looked a certain goal with his first touch.
Instead it was Burnley who thought they had scored a second on 76 minutes, when sub Chris Wood turned in Phil Bardsley's cross - but VAR judged him just offside.
The Burnley striker then beat the offside trap five minutes later to draw a good save from Fabianski and Ashley Westwood fired wide as Burnley had chances to double their advantage. It was West Ham who finished on top, pushing for a late equaliser, but Pope would not be beaten in the pouring rain.
What the managers said...
West Ham boss David Moyes: "I'm disappointed we didn't take something from the game but you have to give Burnley credit for the way they defended. We missed two or three outstanding chances. You don't normally get that number of opportunities to win matches in the Premier League.
"[Tarkwoski's challenge] was only brought to my attention afterwards but, look, it's a red card. It's not going to change the result but it's really disappointing the referee didn't see it as a red, the linesman didn't, and we've got the chance to go to VAR to make a decision on it. We've questioned a few of the decisions against us and had responses back that we don't agree with, so I'm guessing I won't agree with the response this time either. I'm still hoping in the games we've got left that something will go our way."
Burnley boss Sean Dyche: ""It's really pleasing for Jay [to score his 50th goal for Burnley]. He's been a fantastic servant for this club. The back five were outstanding and a willing six in front to go and find a goal. The mentality of the group continues to improve. I think Europe is a big ask, the group is stretched to the limit, but we are still at it."
- Burnley have picked up 13 points from the last 18 available to them in away league games (P6 W4 D1 L1), as many as they earned across their previous 16 such matches on the road before this (W3 D4 L9).
- This was West Ham's 19th Premier League loss of the season; only in 2006-07 (21) and 2013-14 (20) have the Hammers suffered more defeats in a single campaign in the competition.
- Burnley have won back-to-back away Premier League games without conceding for the first time since May 2015.
- West Ham have lost three consecutive league meetings with Burnley for the first time since May 1947.
- Burnley have won back-to-back away Premier League games in London for only the second time, having previously done so back in August 2017. The Clarets have kept a clean sheet in both of those wins, having only kept two shutouts in their previous 24 Premier League away matches at London sides before this.
- Burnley's Jay Rodriguez scored his seventh league goal of the season; only in 2013-14 for Southampton (15) has he ever scored more in a single Premier League campaign.
Burnley visit champions Liverpool on Saturday at 3pm. West Ham travel to face Norwich at Carrow Road on Saturday; kick-off is at 12.30pm.