Bale had only been on the pitch 13 minutes after three months on the sidelines due to ankle ligament damage when he swept home into the far corner seven minutes from time to round off a rapid Real counter-attack.
Alvaro Morata had opened the scoring when he bulleted home Isco's cross 12 minutes before half-time.
"I was happy just to be on the pitch. To get a goal is an extra bonus and thankful to help the team and see the game off," said Bale. "It's been a difficult time but when you get a reception like that it makes it all worth it."
Madrid boss Zinedine Zidane made seven changes to the side that started Wednesday's 3-1 Champions League last-16, first-leg win against Napoli with difficult La Liga trips to Valencia and Villarreal to come in the next week in mind.
"We only have one Gareth Bale," said Zidane. "We are happy to see Gareth back with the team. He is a special player, he gives us something different from the rest."
Marcelo faces hate over Ronaldo, Neymar birthday wish
Meanwhile, Sevilla remain three points behind Madrid as they warmed up for their Champions League clash with struggling English champions Leicester City on Wednesday with a 2-0 victory over Eibar.
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