The home side took the lead at Selhurst Park when Cesar Azpilicueta scored an own goal in the 11th minute.
However, Chelsea drew level seven minutes later when Tiemoue Bakayoko struck an equaliser for Antonio Conte’s men.
Palace, who had not scored a Premier League goal let alone picked up a win this season, then netted a second thanks to Wilfried Zaha’s effort on the stroke of half-time.
Chelsea were unable to find their way back into the game and ended up losing 2-1 as they suffered back to back defeats in the top flight.
And England legend Lineker took to Twitter during the game to comment on how the game was unfolding.
As Palace opened the scoring, Lineker tweeted: “Palace have scored. Yes Crystal Palace…honest.”
And he then added as they went in front again: “Crystal Palace have scored. And this time it’s one of their own players that’s scored. Haha it’s Zaha.”
Chelsea will aim to get back to winning ways when they take on Roma in the Champions League at Stamford Bridge on Wednesday night.
The defeat left Chelsea fourth and nine points behind leaders Manchester City.
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