Sunday's game at the Cardiff City Stadium looked to be heading for a draw when Paulinho scored with a back-heel deep into injury time.
Earlier, Cardiff keeper David Marshall had pulled off a string of outstanding saves to keep his side in the game and Villas-Boas said the three points were fully deserved.
He told Sky Sports: "I think we created so many chances that there could only be one winner today which was Tottenham and it took us some time to get it.
"But throughout the game we created so many chances that we deserved to be leading the game much earlier on.
"So I think it was the right reward for the amount of things that we created.
"We are playing so open and in such an attacking way that we could have left ourselves exposed and ended up suffering but I think today there was justice and we were rewarded in the end."
Early on, Spurs keeper Hugo Lloris appeared to have handled outside the box when he robbed the ball from Frazier Campbell's feet after a poor Kyle Naughton back-pass but he was not sent-off.
Villas-Boas added: "I haven't seen the replay to be fair, if there is any controversy there, but I think it was probably the only moment that he (Campbell) escaped in behind us and we were able to deal with it."