Goals from the in-form Jason Puncheon and defender Scott Dann put Palace into a deserved 2-0 lead at Goodison Park on Wednesday, before Everton fought back with a Steven Naismith goal.
A third from Cameron Jerome sealed the points for the Londoners near the end, meaning that Kevin Mirallas' late strike for Everton was scant consolation.
"It is a great result, but I started at Hull (Palace's first game with Pulis in charge) when I think we had four points, and now we have 40 points. So it's a remarkable achievement from the players.
"The players have been absolutely fantastic - I'm proud of them. Without their effort and their commitment and buying in to what we are trying to do, we wouldn't have achieved it.
"It's a different team to what I had at (former club) Stoke, we have pace and I didn't have too much pace at Stoke. We move the ball really quickly through the pitch, and I thought we did that really well today."
