Bale headed in the first goal of the evening shortly after the half-hour mark and three minutes later provided a fine cross for Karim Benzema to add the second.
The 24-year old gave Madrid more breathing space 20 minutes into the second half by scoring the third goal with his right foot and in stoppage time completed his treble by knocking in a cross from Marcelo with his preferred left foot.
When the final whistle went he collected the match ball and took it to the centre circle, holding it aloft to salute the appreciative public. He has now scored eight goals in the last seven matches for the nine-time European Cup winners.
The win was Madrid's fifth straight in the Primera Division and meant they closed the gap on leaders Barcelona, who visit Athletic Bilbao on Sunday, to three points.
Ancelotti said: "We are playing well at the moment, with continuity and character. The team is focused and has a good attitude. I do not know if it's the best match that we've played. I think recent matches have been very good. We are confident and we want to continue like this. As I said before the match, football is strange. When everything is going well, you can still be surprised."
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