With the Portuguese international sidelined by a slight muscle strain, Bale proved to be decisive as he headed home the opener after Diego Marino could only parry Angel di Maria's cross.
Three minutes later the Welshman teed up Karim Benzema to double Madrid's lead with a wonderful in-swinging cross that the Frenchman bulleted home. Bale grabbed his second of the game when Carlos Pena could only turn Marcelo's cross into the path of the grateful former Tottenham man to slot home.
And Marcelo was again the provider as Bale completed his first hat-trick in Spanish football with a simple left-footed finish a minute from time.
Victory moved Real to within three points of leaders Barcelona and Atletico Madrid, who were also 2-0 victors over Elche on Saturday.
Real boss Carlo Ancelotti said he believes Bale's goalscoring form is evidence that he has firmly found his feet in Madrid. In Ronaldo's absence, Di Maria was given a chance to start and he nearly had the hosts ahead inside five minutes as he smacked a shot off the underside of the bar.
Benzema then fired wide and Di Maria couldn't beat Marino when played clean through on goal as Madrid pilled on the pressure. And it finally told on 33 minutes when Di Maria burst down the left and his cross-come-shot was only parried by Marino into the path of Bale, who headed into the unguarded net.
Moments later Bale was the provider as his sumptuous cross left Benzema with an easy task to head home the second. Madrid continued to dominate after the break and Bale made it three just after the hour mark when he steered home Marcelo's cross on his weaker right foot.
And the 24-year-old was left with the easiest of finishes to round off a perfect hat-trick when he turned home Marcelo's low cross with his left foot.
Atleti ease to win at Elche
Earlier on Saturday, Atletico Madrid moved level on points with Barcelona at the top of the table after goals from Koke and Diego Costa gave them a hard-fought 2-0 win at Elche.
After a first-half devoid of clear-cut scoring opportunities, Atletico took the lead on 63 minutes when Koke bundled home from close range when Manuel Herrera could only parry Raul Garcia's shot from distance.
Costa had endured a quiet afternoon by his standards but he doubled the advantage 11 minutes later as he raced onto Adrian Lopez's through ball before slotting home his 18th goal of the season.
Elsewhere, Celta Vigo beat Almeria 3-1. The visitors took an early 9th-minute lead through Suso but Celta Vigo stormed back with goals coming from Fabian Orellana, Borja Oubina Melendez and Charles.
And the final La Liga match of the day saw Real Sociedad escape Espanyol with a 2-1 victory due to an unfortunate 88th-minute own goal from Christian Stuani. The hosts took the lead in the 31st minute through Jhon Cordoba before Sociedad drew level in the 69th minute with a fine effort from Antoine Griezmann.