Jermain Defoe put Spurs in front in the 58th minute at Villa Park before Bale blew the home team away with goals in the 61st, 73rd and 84th minutes to take his tally to nine in the English Premier League this season.
Asked by reporters if there were any better players in the game than the Welsh international, Villas-Boas replied: "He is up there with the best.
"His finishing is very accurate. He has been prolific in front of goal this season and I think he is enjoying getting into those positions.
"His left foot is wonderful and the power and direction he applies on the ball is wonderful too," added the Portuguese after victory lifted Spurs to fourth spot, 13 points behind leaders Manchester United.
"I think he is improving every day - he is such a young player," said Villas-Boas. "He is one of our major assets.
"The team changes so much from one year to another and as he keeps learning he will feel even better and probably his performances will improve."
Villas-Boas said Defoe's goal, his 10th in the league this season, was especially significant for Spurs after Villa had been on the receiving end of an 8-0 battering at Chelsea on Sunday.
"It was important to get that goal because we knew emotionally it could ... make Villa unstable in some way," he explained.
Villa manager Paul Lambert said his 16th-placed side were fortunate to go into halftime at 0-0.
"We rode our luck massively in the first half because Spurs were very good," said Lambert who was confident his squad would recover from their two heavy defeats.
"They will be fine," he said. "Whether we win, lose or draw ... we always try to treat them the same way and try to keep their spirits the same.
"One thing in football is that you can't dwell on it and you have to bounce back. There is no other way." (Writing by Tony Jimenez; editing by Greg Stutchbury)
- Sports & Recreation
- Jermain Defoe