Marcelo Bielsa's side, who were beaten by the same scoreline at home to Leicester City on Monday, slumped to 14th place with the loss while Palace moved up to sixth, on 13 points from eight games, just three points behind leaders Southampton.
Scott Dann headed Palace into a 12th minute lead with a thundering header from an Eberi Eze corner.
Leeds thought they had drawn level with a nice finish from Patrick Bamford but the effort was ruled out for a narrow offside by VAR.
After that let-off, Palace doubled their lead with a brilliant free kick from Eze, his first goal for the club, as he struck a 20-metre shot into the top corner.
Bamford did score with a confident drive after being set up by midfielder Mateusz Klich's headed pass when he buried the ball in the bottom corner for his seventh goal of the campaign.
But Palace restored their two-goal advantage just before the interval when Helder Costa's sliding tackle deflected a low cross from Wilfried Zaha inside the near post, confounding Leeds goalkeeper Illan Meslier.
Zaha also had a hand in Palace's fourth, running at the Leeds defence before slipping the ball to Jordan Ayew who made no mistake.
Leeds have conceded 17 goals this season, more than any other team in the league, an issue Bielsa must urgently address.
Palace boss Roy Hodgson was understandably pleased with a rare goal feast from his team.
"It was a highly competitive game. We played well and were good value for our victory," he said.
"It was a good win against a team that has started so well and has a style of play which is different to what we're used to seeing. In terms of our attacking play, we were excellent."