With the Portuguese 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
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 .
Bale claimed he didn't feel any added pressure in the absence of Ronaldo, but admitted to being desperate to seal his first Madrid hat-trick after registering his second of the evening with still 26 minutes to go.
"I didn't feel any pressure to be honest, I just want to go out there and enjoy my football and play as well as I can. I always try to do that and thankfully I got a hat-trick.
"I think as soon as I scored the second I was trying to get the third, I was trying my hardest to get into positions and thankfully the move did work out and it was a great ball by Marcelo to put it on a plate for me."
Real boss Carlo Ancelotti said he believes Bale's goalscoring form is evidence that he has firmly found his feet in Madrid.
"I think that his adaption period has finished as I said yesterday.
"He is a very important player for us, he is playing with confidence and he did very well today."
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 piled 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.
Earlier, Atletico 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.
Atletico boss Diego Simeone had recalled six first-team regulars rested for Tuesday's 1-1 draw away to Zenit St Petersburg in the Europa League.
However, he recognised that it wasn't until the introduction of Garcia and Adrian in the second-half that Atletico began to take control.
"It is a very important victory against a very difficult opponent," he said.
"We started well in the first-half but then Elche had two or three dangerous counter-attacks. At half-time we talked and saw that we needed to use the wings more. The introduction of Raul Garcia and Adrian gave us the creativity we needed in the tightest moments of the game."