Karim Benzema also got on the score-sheet for los Blancos, while Mario and Giovani dos Santos replied for the visitors
Bale returned to the starting line-up after missing the last three games with a leg injury, and put in a virtuoso performance at the Bernabeu, scoring the first and setting up the second for Benzema.
Mario reduced the arrears before half-time, but Jese and Benzema added further goals for Real either side of Giovani dos Santos' sublime free-kick, ensuring Real did not feel the absence of Cristiano Ronaldo, who started a three-match suspension.
It took just seven minutes for Bale to make his mark on the game as he robbed Dorado of possession before proceeding into the box and dinking delightfully over Sergio Asenjo.
Despite their superb start, Real were given a huge let-off soon after when Jonathan Pereira blasted over the crossbar having been left unmarked in the box.
Madrid were dealt a blow when full-back Marcelo limped off with an apparent groin injury, to be replaced by Fabio Coentrao.
Bale tormented the Villarreal defence once more when play resumed and created the second on 25 minutes, effortlessly skipping past Jaume Costa on the right and clipping a cross from the byeline to Benzema, who prodded home at the near post.
Villarreal could perhaps consider themselves unfortunate to be two goals adrift, but Mario halved the deficit in superb fashion three minutes shy of the break.
The full-back took one touch to burst into the hosts' box before unleashing a fierce right-footed strike into the far corner.
Ancelotti's men dominated possession after the restart, and full-back Daniel Carvajal came close to restoring his side's two-goal cushion as he dragged a shot narrowly wide of the far post.
Shortly before the hour mark Benzema had legitimate claims for a penalty rejected when he appeared to be bundled over by Dorado.
It mattered little, however, as Jese made it 3-1 on 64 minutes.
A neat exchange between Angel Di Maria and Benzema led to the former slipping a neat throughball to Jese, who guided the ball past Asenjo with the outside of his boot.
With just over 20 minutes remaining, Dos Santos bent home a sublime free-kick from 25 yards.
But on 76 minutes Benzema drove home from the edge of the box after more good work from Jese.