Casemiro opened the scoring for the Spanish champions in the first half before Asensio and then Isco scored after the break to give Real their first win in three games in all competitions.
The victory took Real above neighbours Atletico, who also have 23 points, on goal difference into third spot, four off Valencia and eight adrift of Barcelona.
“We came out looking for the win, they sat deep but then once we scored we were able to hit them on the counter,” said Real Madrid captain Sergio Ramos.
“We were clinical in front of goal and the win comes at a good time for us. We go into the derby (against Atletico) next time out with a win under our belts.”
With their title rivals winning on Saturday, the pressure was on Madrid heading into the international break after a shock 2-1 defeat at Girona in their last Liga game and a 3-1 midweek reverse away to Tottenham Hotspur in the Champions League.
However, after a nervy opening period, Real's class showed.
TENSION RELEASED
Karim Benzema missed their best chance after three minutes when he fired straight at keeper Raul Lizoain. Nacho then went close before Cristiano Ronaldo - who has one Liga goal this season - clipped the outside of the post with a left-foot shot.
Casemiro’s goal came at a good time for the home side, with the interval fast approaching, and released the tension around the Bernabeu when he stooped to nod home Asensio’s corner.
From there on it was plain sailing for Zidane’s side.
There appeared little danger when the ball fell to Asensio outside the box after 56 minutes but he thundered an unstoppable left-foot strike into the top corner.
Ronaldo went close again and Ramos struck the bar before Isco rounded off the scoring with a sweeping move on the break 15 minutes from the end. Late on there were a smattering of boos for French striker Benzema as he was substituted.
However, Ramos said they were not unduly concerned about a lack of goals from Benzema and Ronaldo so far this season.
“Their goals will come. Karim is more generous in that sense. Cristiano goes home annoyed when he doesn’t score, but we’re not worried. They make the difference and the most important thing is to win. The goals will come.”
Las Palmas remain second-bottom on six points.
(Editing by Ken Ferris)
