An under par Spurs side were dragged over the line by the in-form winger, whose fine season continued in the first leg of their round of 32 tie at White Hart Lane.
Bale fired home another stunning free-kick in stoppage-time to give Villas-Boas' side a 2-1 lead heading to central France.
"Incredible," the Portuguese said. "Not only his all-round game but the ability he has to strike these free-kicks.
"The ball gains so much power when he strikes it and it changes direction very, very easily. Today we saw not only two great moments of brilliance but three as their goal was absolutely fantastic, too.
"It played out to be an excellent game. Maybe the first half was a little more exciting as in the second half both teams struggled to get the ball on the ground and get it moving.
"It was a bit sloppy but we saw some moments of individual brilliance and Gareth was fantastic once again."