Late substitute Sergio Araujo scored a dramatic equaliser six minutes from time to earn Quique Setien’s side a point and condemn Madrid to a second LaLiga draw in four days.
Marco Asensio put Los Blancos ahead after 33 minutes but the home side were level just five minutes later when Tana took advantage of some loose defending to score.
Karim Benzema replaced Asensio as Zinedine Zidane went on the attack after 65 minutes and the France striker scored his second goal of the season from close range to put Madrid back into the lead.
But, playing without injured duo Marcelo and Casemiro, the visitors were not at their best defensively and they were exposed again in the 85th minute when Araujo evaded goalkeeper Kiko Casilla to earn Las Palmas a positive result.
The home team’s goalkeeper Javi Varas made a good early save when Alvaro Morata was allowed a free header at goal from Toni Kroos’s free-kick, and the home side were relieved to see Cristiano Ronaldo fail to control a pass from Morata when the Portugal ace was ideally placed to score.
Madrid restricted Las Palmas to tentative attacking forays and long-range shots early on, while Morata was given precious little quality service at the other end and had to feed on scraps.
Casilla was finally tested when Tana flicked Jonathan Viera’s chipped ball towards goal, and again when Tana shot from distance, but the goalkeeper was equal to both attempts.
With conventional routes to goal proving fruitless, Madrid took the lead when defender Nacho hurtled down the left flank and struck a shot that Varas could only parry. The rebound rose perfectly onto the head of Asensio, who nodded the ball home.
Five minutes later, Momo sent over a cross that evaded Raphael Varane and Tana had time to collect the ball in the box, control it, and fire a low show into the corner of Casilla’s net to make it 1-1.
Gareth Bale looked Madrid’s most potent attacking threat and he tested Varas with stinging shots at the end of the first half and the start of the second, drawing good saves from the busy Las Palmas keeper.
Ronaldo had the ball in the net after 56 minutes only for the attempt to be ruled out for offside, and Zidane sent on Benzema for Asensio just after the hour mark.
The former Lyon man had a chance to score with his first touch but shot tamely at Varas when Kroos’s corner fell to him inside the six-yard box.
Two minutes later Morata broke down the middle and fed Ronaldo, whose shot was parried by Varas straight into the path of Benzema, the France striker lashing the ball high into the net.
When Zidane took Ronaldo off it looked like the result was safe, but Las Palmas ventured forward in the 85th minute and Aythami’s superb knock-down found Araujo.
The forward hit a shot that came back off Casilla and he collected the rebound to bundle the ball home, earning his side a share of the spoils and condemning the heavyweight visitors to more frustration.