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 yesterday.
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.
Victory moved Real to within three points of leaders Barcelona and Atletico Madrid, who were also 2-0 victors over Elche on Saturday.
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.
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."
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