Karim Benzema, who was also a second-half substitute, netted a second for Real Madrid in the 67th minute as the visitors looked to be returning to winning ways in Spain's top flight, but Araujo's close-range finish five minutes from time secured a point for the Yellows on home soil.
The first half-chance of the match fell to Real Madrid inside four minutes, but Cristiano Ronaldo could only fire wide of the post after finding a route past Las Palmas's Brazilian defender Michel down the left, before Toni Kroos tested the handling skills of Javi Varas with a low strike in the sixth minute of action.
One minute later, Alvaro Morata, who was given the nod over Benzema at centre-forward, tested Varas with a close-range header, but the home side's goalkeeper was once again equal to it.
It was the visitors that continued to look the most likely to make the breakthrough and after having two penalty appeals turned down, Ronaldo had a couple of chances of his own - first fluffing his lines from a Morata cross inside the box, before missing the left-hand post from distance.
Las Palmas's first opportunity arrived in the 20th minute when Dani Castellano broke down the right before delivering a smart cross in to Jonathan Viera, but the attacker could not produce a clean strike and it went behind for a goal kick.
Real Madrid again came close in the 25th minute when a scramble inside the box led to Morata and Ronaldo both having opportunities, but David Garcia and Aythami Artiles made important blocks. The Yellows were also a threat, however, and Real Madrid stopper Kiko Casilla had to keep out attempts from Tana and Viera as the first period developed.
The match was so open that the first goal was bound to arrive, and it came for Real Madrid in the 33rd minute when Marco Asensio, who was chosen ahead of Isco and James Rodriguez, headed home from close range after Nacho's low strike had been saved by Varas.
Las Palmas responded just five minutes later though as a dangerous cross from Momo found Tana inside the Real Madrid box and the Spaniard settled before carefully placing the ball into the bottom corner.
Ronaldo set up an opportunity for Bale early in the second period after a quick counter-attack from the visitors, but the Welshman's low strike was once again saved by the impressive Varas.
Real Madrid had the ball in the back of Las Palmas's net for a second time in the 56th minute, but the flag was raised when Ronaldo finished from close range after another smart run and pick-out from Bale.
Las Palmas had a couple of half-chances to register either side of the hour mark, but Nabil El Zhar, who replaced the injured Viera, fired wide of the post, before Vicente Gomez's low strike was kept out by Casilla.
Seconds after his introduction, Benzema had a golden chance to register for Real Madrid after a towering header from Raphael Varane fell for the Frenchman, but his effort was straight at Varas from close range. Benzema was not to be denied, though, and scored in the 67th minute after Varas had palmed a Ronaldo effort into the striker's path.
Ronaldo played a key role in Real Madrid's second goal, but it was a difficult night for the Portuguese and he was replaced 18 minutes from time in a decision that did not go down well with the 31-year-old.
Real Madrid looked to be easing towards all three points in Gran Canaria, but Las Palmas continued to threaten and equalised in the 85th minute when Araujo turned home from close range after the ball fell for the striker following an initial smart save from Casilla.
Next up for Real Madrid, who came close to winning it late on through Benzema and Isco, is a trip to Borussia Dortmund in the Champions League on Tuesday, before they return to La Liga action at home to high-flying Eibar next weekend. Las Palmas, meanwhile, are next in action away to Osasuna next Saturday.