Zinedine Zidane's men could ill-afford another loss after Barcelona went 11 points clear of them by beating Sevilla 2-1 on Saturday, but they rarely looked in trouble, showing a significant improvement from their Champions League loss to Spurs on Wednesday.
Madrid spent much of the first half on the front foot and created a host of chances, with Karim Benzema wasting a glorious opportunity early on and Cristiano Ronaldo - who endured another frustrating day in front of goal in LaLiga - going on to hit the post.
Las Palmas' resistance was finally ended by Casemiro just before the break, with the Brazilian's goal the first header scored by Madrid in any competition this season.
Asensio effectively wrapped things up early in the second half with a ferocious effort from 25 yards.
And Isco completed the scoring with an easy finish from Ronaldo's cross in the 74th minute, handing Las Palmas a seventh successive league defeat, while Madrid moved back up to third.
It took just four minutes for Zidane's side to carve the visitors open and create the first chance, but Benzema's finish was one of a player lacking confidence, as the French striker shot straight at Raul Lizoain when one-on-one.
Las Palmas almost made them pay for that miss a few moments later, Vitolo charging into the right side of the area and forcing Kiko Casilla into an important stop.
The hosts remained the dominant force, however, and felt aggrieved not to be awarded a penalty in the 24th minute when Isco's chipped pass appeared to strike the arm of Ximo Navarro.
Las Palmas then had the frame of the goal to thank shortly after, as Ronaldo saw his curling left-footed effort clip the outside of the left-hand post from 18 yards.
The breakthrough eventually came four minutes before half-time, Casemiro heading in from six yards after a corner was deflected through to him.
Las Palmas were more purposeful at the start of the second half and felt they should have had a penalty when Vitolo appeared to be pulled back by Casemiro.
And Madrid took full advantage of that let-off in stunning fashion just before the hour mark.
The visitors cleared a free-kick as far as the lurking Asensio and he lashed an unstoppable half-volley into the top-left corner from 25 yards.
Ronaldo showed signs of frustration as his poor league form in front of goal continued, but he did make a telling contribution 16 minutes from time, crossing in for Isco to tuck in a third.
Madrid probably should have been awarded a late penalty when Mauricio Lemos tripped Nacho Fernandez in the box, but it had no impact on the end result, as the hosts confidently secured all three points.
