Wales forward Bale was making his first Madrid start since November after injuring his ankle, and his header sparked a stunning revival after Manu Trigueros and Cedric Bakambu had put Villarreal 2-0 up.
Bale was taken off in the 89th minute, but head coach Zidane insists the change was merely a precaution.
"He's just picked up a knock, that's all there is to it," Zidane told reporters.
Madrid levelled the match with 16 minutes remaining through a Cristiano Ronaldo penalty that saw him become the all-time leading scorer of spot-kicks in La Liga, after Bruno Soriano was harshly penalised for handball.
Alvaro Morata's header then won the match for Madrid at Estadio de la Ceramica to ensure they stayed one point clear of Barcelona at the top of the table with the added bonus of a game in hand.
Zidane stated that his players were convinced it was a handball against Soriano, but the Frenchman refused to offer his opinion.
"The players have said that it was a handball," he added. "I didn't see it from where I was and I'll never interfere with refereeing decisions. He awarded it and that's that.
"We performed much better in the second half than we did in the first. We got into more scoring positions and ultimately we come away with three points against opposition that can make life tough for you.
"We're happy to have taken three points against a great side."
Zidane also emphasised the importance of Madrid's comeback particularly given they were beaten 2-1 by Valencia last time out in La Liga.
"At 2-0 down we had to change something. We did so and it worked out well for us. We made an attacking change and enjoyed more possession in their half," said Zidane, whose Madrid side scored in their 44th consecutive match in all competitions to equal the record for Spanish clubs set by Barca in 1944.
"We knew that we were coming up against a good side, who have being doing fantastically well at home. We had to be patient and our substitutions ended up changing the game.
"It was important for us to get the three points to remain top."