Tottenham produced a strong second-half performance to take all three points and go five clear of second-placed Manchester City who don't play until Sunday afternoon.
Palace captain Joel Ward deflected a way-ward James Maddison strike into his own net to give Spurs the lead before substitute Brennan Johnson announced his presence with his first assist for the club for Son Heung-min’s eighth goal of the season and the club’s seond on the night.
Before that, Tottenham had gone the entire first half without a shot on target in one of the most disappointing 45 minutes under Ange Postecoglou.
But as has often been the case since the Australian manager took over, he rectified the situation by taking off Ben Davies for Emerson Royal which instantly improved the passing and shape of the team.
Spaces began to spring up for Pape Matar Sarr who was involved in the first goal, this time it was his switch that caught the Palace backline off guard and gave Johnson the space to calve his assist for the Son goal.
Jordan Ayew then volleyed home a goal for the Eagles to set up a nervy end to the game, VAR had a long look at the goal after the ball appeared to hit his hand, but it concluded it was good enough to stand.
There was also the first minutes of the season for Rodrigo Bentacur who was introduced late on for his first taste of football since his knee injury back in February.
For large parts of the game, Tottenham looked comfortable but had to hang on to grind out what was their eighth win of the season.
1. Guglielmo Vicario -6
Came for two crosses in the first half. Looked assured even when under immense pressure.
2. Ben Davies -5.5
Replaced Udogie in the team and lasted only first half.
3. Micky van de Ven -7
Should be in the discussion for signing of the season. Has underrated pace but it is his reading of the game that is a thing of beauty.
4. Son Heung-Min -8
Somewhat very quiet first half for the Tottenham captain before he made up for it with a good finish to put Spurs two up.