Spurs struggled to break down a stubborn home side in the first half but got their breakthrough when Joel Ward turned James Maddison's cross into his own net in the 53rd minute.
Heung-min Son's eighth goal in ten League games capped a fine move and sealed the points for Spurs, who remain unbeaten and increasingly feel like the real deal.
Jordan Ayew set up a nervy finale by rifling in a brilliant strike in stoppage time but Spurs held on to move five points clear for the first time in Premier League history.
Here's how we rated the Spurs players at Selhurst Park...
Guglielmo Vicario 7
Maintained his fine form with sharp stops from Jordan Ayew and Odsonne Edouard in the first half and commanded his area well.
Pedro Porro 6
Involved in the build-up to the opening goal and assured in possession but caught out for Ayew's late goal.
Cristian Romero 8
Booed throughout for the crime of being fouled by Edouard but composed on the ball and did not put a foot wrong at the back.
Micky van de Ven 8
His pace was important in sweeping up, particularly behind Davies in the first half. Lightning quick and imposing.
Ben Davies 4
His pace was exposed once or twice by long balls, forcing van de Ven to cover, and he did not look comfortable inverting. Spurs missed Destiny Udogie.
Pape Sarr 8
Influential in both goals, bursting to the touchline ahead of the first and switching the play to Johnson for the second. Outstanding.
Yves Bissouma 7
Excellent at wriggling out of tight spaces and playing under pressure. Withdrawn early, presumably to save him from a booking which would have ruled him out of Chelsea.
James Maddison 8
Wanted too many touches in the first half but came alive after the interval to make the difference. His fierce cross bounced off Ward and into his own net before his smart one-two with Johnson created the clincher.
Dejan Kulusevski 6
Struggled to make inroads in the final third but worked hard and held up the ball well.
Created Spurs' best openings of the first half with a smart pass around the corner for Maddison and a knock down for the playmaker. Dragged a shot of his own wide, and was bright if a little clunky.
Heung-min Son 7
On the scoresheet again with another instinctive, poacher's finish. Thriving in a new phase of his career as a lethal No.9.
Emerson Royal (Davies 45') 7
More solid than Davies despite playing on his unfavoured side and involved in some dangerous attacks.
Pierre-Emile Hojbjerg (Bissouma 64') 6
Another professional display in the middle, as Spurs saw out the game by keeping possession.
Brennan Johnson (Richarlison 64') 7
Came off the bench to make an instant impact, exchanging passes with Maddison before squaring for Son's goal. Stretched Palace with his pace.
Rodrigo Bentancur (Kulusevski 89') 6
Returned to the pitch for the first time since rupturing his ACL in February. A hugely positive finish to a great night for Spurs.
Bryan Gil (Maddison 89') 6
First minutes of the season, another welcome return.
Not used: Forster, Skipp, Dier, Lo Celso.