A Manuel Lanzini strike and a missed penalty by Christian Benteke condemned Palace to defeat in a rain-soaked encounter at Selhurst Park.
The Argentinian midfielder netted after 18 minutes after sneaking into the area unmarked to finish off a good move, but on the stroke of half-time Benteke won a penalty but sent it wide of the target.
He would hit a post too before half-time but despite the Hammers playing the final 15 minutes with 10 men after Aaron Cresswell was dismissed for two yellow cards, the Eagles couldn’t conjure up an equaliser.
Slaven Bilic sprung a surprise by setting his team out in a 3-5-1-1 formation which caused Palace a few problems early doors. Cresswell galloped down the left and thrashed a shot into the side-netting after just three minutes and Simone Zaza scuffed a tame attempt straight at Steve Mandanda soon after.
The Eagles’ first opportunity was a good one but Jason Puncheon’s clever pass into Wilfried Zaha saw the winger drag it wide of the far post, however the Hammers continued to look more dangerous in the opening 15 minutes and Cheikhou Kouyate flashed a header from a Dimitri Payet corner just wide of the mark, however their pressure told as they found the breakthrough in the 18th minute.
Cresswell and Payet linked up on the left flank and the full-back, spotting the run from deep by Lanzini, played a fine first-time cross which was begging for the Argentinian to tuck it past Mandanda, which he did to score for the third game in a row against Palace.
As the rain poured down, the chances dried up with the game turning into a midfield battle with neither side giving each other a sniff of a chance, and two minutes before the break Lanzini had a drive from 30 yards but it was once again straight down the throat of Mandanda, but 60 seconds later the Eagles were given a lifeline when they won a penalty.
After Zaha was felled just outside the box, the ball continued into the box and Benteke nipped in ahead of Angelo Ogbonna who brought him down, and the red-hot Belgian stepped up to take it but his stuttered run-up saw him slice it wide of the top corner and into the stunned fans in the Whitehorse Lane end.
However he nearly atoned for his error just a minute later with the final action of the half, when he managed to strain and get his head to a cross but he saw it clip the post with Adrian sprawling in desperation as he escaped into the break with his clean sheet somehow still intact.
At half-time Alan Pardew altered things by bringing on Zeki Fryers and Yohan Cabaye and the Frenchman saw a shot drift wide 10 minutes after his introduction, and the positivity after the break continued as Andros Townsend took aim from 25 yards but couldn’t find enough curl on his effort to trouble Adrian.
Jason Puncheon was next to warm the gloves of the Spanish keeper on 71 minutes when he drove forward from the centre of the park but his grasscutter lacked the required power, but he was in the right place when he managed to scramble the ball off the line when a corner was nodded goalwards by Michail Antonio but Puncheon remained on the post to clear.
But the game took another twist when the visitors were reduced to 10 men. Cresswell was booked for a dive in the area when he went in for a challenge with Cabaye, and then 60 seconds later he was heading down the tunnel after bringing down Zaha in full flight, handing Palace a numerical advantage for the final quarter of an hour.
Benteke had another opportunity but he headed over the top from a Puncheon corner, but in injury-time Adrian made a brilliant reaction save when Connor Wickham’s header was tipped over by the Hammers keeper and ensure the east Londoners won only their second league game of the campaign.
Palace: Mandanda, Ward, Delaney, Tomkins, Kelly (Fryers 46), McArthur (Wickham 70), Ledley (Cabaye 46), Zaha, Puncheon, Townsend, C. Benteke. Subs not used: Hennessey, Sako, Lee, Campbell.
West Ham: Adrian, Kouyate, Ogbonna, Reid, Antonio, Obiang, Noble, Cresswell, Lanzini (Nordtveit 88), Payet (Fernandes 79), Zaza (Calleri 86). Subs not used: Spiegel, Collins, Feghouli, Fletcher.