Las Palmas looked to have secured a deserved point when Willian Jose cancelled out a first-half Sergio Ramos header in the 87th minute, but Real Madrid, who had Ramos sent off in second-half stoppage time, found a second to ensure that they would move four points behind second-placed Atletico Madrid in the table.
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Las Palmas boss Quique Setien made just the one change from his team's 1-0 win at Villarreal last weekend and it came in the final third as Roque Mesa took the place of Nabil El Zhar, who dropped to the bench.
The first strike of any kind came from Ronaldo in the eighth minute, but the Portuguese's effort was always moving away from the target, much to the frustration of Bale, who had found space down the left.
Down the other end, Willian Jose had a chance to score against his former club after a mistake from Luka Modric, but the Brazilian could not beat the advancing Keylor Navas inside the Real Madrid box, before Momo fired over the crossbar from a tight angle.
Ronaldo had a golden chance to send the visitors ahead in the 24th minute when he went through one-on-one with Javi Varas, but the Las Palmas stopper made a smart save. Varas could do nothing from the resulting corner, however, as he watched Ramos produce a header from an Isco delivery to make the breakthrough in Gran Canaria.
Ronaldo came close to scoring a second for Los Blancos in the 30th minute when he met a Vasquez cross inside the Las Palmas box, but his low strike was just deflected wide of the post.
In the 32nd minute, Pedro Bigas might have done better for the hosts when he met a corner from the left, but the centre-back's effort was always too high of the crossbar during what was an end-to-end period of the match.
Ramos continued to venture forward in the latter stages of the first period and had another half-chance five minutes before the break, but the centre-back's close-range strike was blocked as Real Madrid took a one-goal lead into the break.
Las Palmas came out firing after the restart, but neither team had a chance of note in the opening 15 minutes of the second period and temperatures were raised on more than one occasion following a couple of tasty challenges.
Arbeloa almost turned past his own goalkeeper in the 62nd minute following a dangerous free kick, but Navas got down to make the save as the visitors kept their one-goal, but far from convincing, lead intact.
Nili was next to come close for Las Palmas in the 66th minute after super work from Momo, but the youngster took too long to release a strike, which allowed Navas to close the space and make the save.
The referee controversially pointed for an indirect free kick inside the Real Madrid box 15 minutes from time, but Casemiro stuck out his leg to direct a low Momo strike wide of the post.
Las Palmas introduced their top scorer from last season, Sergio Araujo, in the 85th minute and the striker almost had an equaliser seconds after entering the field, but he headed a Bigas cross over from close range.
The home side did indeed make it 1-1 in the 87th minute when Willian Jose netted from close range, but Real Madrid were back ahead two minutes later when Casemiro headed home from a corner.
Las Palmas continued to press late on and had a one-man advantage when Ramos picked up a second yellow for a late challenge on Momo, but the visitors held on to secure all the points following an incredible finish in Gran Canaria.