Glenn Murray scored twice, either side of Scott Dann's header, and was sent off in an eventful afternoon for the Palace striker as his side climbed to the relative safety of 12th.
Enner Valencia scored for West Ham after 76 minutes but it was too little too late for the Hammers whose season is unraveling after earlier challenging for the top four.
"Up until the sending off, we were in total control, but we don't make it easy for ourselves," Pardew, who left Newcastle United to take over at Palace, told Sky Sports.
"We saw it out and we had some scary moments but it was nothing less than we deserved."
Murray's header, helped in by West Ham's Aaron Creswell's attempted clearance, gave Palace a fortuitous lead in the 41st minute before Dann doubled their advantage in the 51st minute with a powerful header.
Murray, in the thick of the action all afternoon, added his second in the 63rd minute with a glancing header but was dismissed six minutes later for a second yellow card just moments before Pardew had planned to substitute him.
"It was a mixed afternoon for him wasn't it," Pardew added. "He could have had a hat-trick in the first half. He gets into the right positions.
"The sending off was a little bit unlucky because we were just about to sub him off. He has to go for the ball, and I don't think he deserved that. I spoke to him at halftime. We all knew he was on a knife edge.
"But I'm absolutely delighted with him. He was terrific. It shouldn't take away from a terrific performance."
Valencia's goal was scant consolation for West Ham who have won just two of their last 12 league games since climbing to fourth in mid-December.
"I'm shocked," West Ham boss Sam Allardyce, whose future at the club has again been the subject of speculation, told the BBC. "Our level of performance wasn't where I expected it.
"It's disappointing when we've built expectation levels so high at home. It's about the basics, really. If we don't play to our best, we'll struggle.
"We warned the lads about Crystal Palace's set plays because 50 percent of their goals have come from set-plays. And we've conceded from two corners and a free-kick."
(Reporting By Tom Hayward; editing by Martyn Herman)
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