Both managers lavished praise upon the Welshman's contribution to Spurs' 2-1 win as the winger provided an assist and a goal to help win the game and delight his boss
The north London side saw off the Swans thanks to early goals from Jan Vertonghen and Bale, despite late pressure after Michu pulled a goal back for the home side.
The Welshman had a hand in both of Spurs' goals as he set up the first and netted the second himself, before preventing a Swansea equaliser late on, leading Villas-Boas' to wax lyrical about the winger, as well as his side's overall performance.
"When there are so many things that go well for the team, it is hard to single out individuals but Gareth [Bale] is a world class player offensively and defensively, as he showed when he made the block at the end to prevent Swansea getting a draw," he told reporters.
"But the whole team deserve credit because coming here after two league defeats and playing the way we did is never easy. We spoke at half-time about trying to get the third goal to put it beyond doubt but we couldn't and they did well to come back.
|9/1||Tottenham are 9/1 with BetVictor to beat Everton 2-1 next weekend|
"We showed great determination and the winning mentality that surrounds us to come away and hold for a great win from home and put ourselves back on track."
Michael Laudrup, meanwhile, was also generous in his praise of Bale, deeming the Welshman to be the difference between the sides as he lauded his "exceptional" contribution to the contest.
"They had a very good start but both goals showed a player of Gareth Bale's quality can make the difference. There are different players, even at this level," he told reporters.
"There are good players, very good players and exceptional players and they are ones who sometimes, out of nothing, can make a difference.
"If you see his goal today, or his goal against West Ham, it was not even a chance. He is a player who makes the difference and you are lucky if you have that. Not many teams do. If you take Bale out, without him, the teams were at the same level."