Manager Dean Davenport was ecstatic with his side's performance.
“It feels fantastic," he said. "I thought in the first half we were outstanding. To go into half-time 2-0, it was fully deserved.
“I thought the players showed themselves in a good light and we were exceptional in the way we defended our goal.
“We beat the leaders of the league and not many teams in our league will do that because Durham are a very good side.”
Palace got off to an excellent start and took the lead only three minutes into the game. Bianca Baptiste was gifted the ball and smashed it into the bottom corner.
Durham responded well after a shot from Danielle Brown went just wide and Sarah Robson’s header was saved by Palace 'keeper Emily Orman.
Palace looked to extend their lead further after Kirsty Barton found Shiv Wilson in the box, but her shot was fired just wide of the post.
It was the Eagles who doubled their lead after Leigh Nicol’s through-ball to Wilson; her resulting shot was sent past Durham 'keeper Megan Borthwick.
The visiting Wildcats continued to push, with Danielle Brown picking Mollie Lambert out in the box but her close range chance was met by Orman.
Palace went into the halfway stage with a two-goal advantage over Durham, ending the visitors' five game streak without conceding.