Tottenham had not lost in their seven Premier League matches before the midweek game, but Christian Eriksen's fantastic goal settled the contest between the South and North London sides.
The win ensured that Chelsea's lead at the top of the table was cut to four points with the Blues in 78 points after Tuesday's 4-2 victory against Southampton.
First chance of the game went the way of Tottenham HotSpur and Hary Kane. The England man took a touch on the edge of the area but his shot was charged down by Palace who piled on some early pressure.
Spurs fought back but Kenya international Victor Wanyama was yellow-carded in the 26th minute of the first half while Christian Eriksen has a low shot blocked by Mamadou Sakho four minutes later.
Moussa Dembele gave way for Heung-Min Son at the start of the second half. Samuel Allardyce was also forced to make a change as Mamadou Sakho was unable to continue due to injury, Damien Delaney came on in his place for the hosts.
Dele Alli came close to scoring for Spurs in the 59th minute. He beat his marker and got on the end of a cross from Kyle Walker, but he hit a shot just wide of the right post.
The pressure from Spurs forced Palace to be ultra defensive in approach and it paid off with only eleven minutes left on the clock when midfielder Christian Ericksen scored.
The Dane received a pass, made some space for himself and unleashed a long-range shot past Palace goalkeeper Wayne Hennessey and into the bottom left corner.
Toby Alderweireld tried a spectacular half volley but his shot was cleared within the last ten minutes of the match. Seven minutes was added after full time and Dele Alli was substituted late on by Kevin