It was redemption for the Palace ‘keeper, who had been at fault for Harry Kane’s first half-opener in SE25.
Spurs – showing 10 changes from the Europa League win over Antwerp – made a positive start to proceedings, but Palace possessed an obvious threat on the counter-attack as Toby Alderweireld blocked a strike from Wilfried Zaha before at the other end Heung-min Son drifted in behind Cheikhou Kouyate to fire against the stanchion.
Hugo Lloris then made a fine low stop to keep out Zaha’s skidding, deflected low strike that zipped menacingly across the greasy surface, with Palace’s talisman looking in the mood as he rushed a shot into the stands under pressure.
Guaita did brilliantly to deny Tanguy Ndombele and also kept out Kane’s header from a corner after Sergio Reguilon’s deflected effort with his weaker right foot had whistled narrowly over the crossbar.
Tottenham went ahead after 23 minutes, with Guaita going from hero to zero in a flash as he made a mess of Kane’s long-range strike from a central position that swerved before going in off the hand of the Spanish ‘keeper, who should have done much better.
Another goal combination between Kane and Son took them to 12 for the season – one shy of the Premier League record for a single campaign.
Kane blasted a free-kick well wide and then bravely headed away Eberechi Eze’s effort from his position in the wall, with Guaita trying to redeem himself by diving at the feet of Steven Bergwijn and then making another impressive save from Ndombele.
Patrick van Aanholt had a low free-kick blocked by Son before the hosts came agonisingly close to drawing level shortly before the interval, with Eze expertly cutting inside Alderweireld before bending a shot against the base of the far post.
Spurs started the second half brightly, with Zaha blasting over after a one-two with Christian Benteke, though the offside flag had already been raised.
The Ivorian international then shook off an impact injury following a collision with Alderweireld to curl over again as Palace began to dominate proceedings in search of an equaliser.
Pierre-Emilie Hojbjerg smashed wide from 35 yards out and Schlupp was then guilty of missing Palace’s best chance of the game, slipping and getting his close-range finish all wrong after Christian Benteke and James McArthur had flicked on captain Luka Milivojevic’s free-kick.
Benteke landed a header on the roof of the net and also headed straight at Lloris before Palace’s determination finally paid off.
Schlupp was on hand to atone for his earlier miss as he turned the rebound home from close quarters after Eze’s free-kick had bounced off an unsighted Lloris.
Speaking of making up for errors, Guaita produced two fine saves late on to keep out Kane’s goalbound header from an Aurier drive and Dier’s well-struck free-kick after substitute Dele Alli had been fouled by Kouyate.
A deserved point moves Palace up to 11th, while Tottenham will hope for a favour from Fulham as they take on Jurgen Klopp’s defending champions at Craven Cottage.