Spurs dominated large passages of the game at Cardiff City Stadium, and registered 29 shots to Cardiff's six, but were in danger of failing to capitalise as they found home goalkeeper David Marshall in fine form.
The Scotland international made a string of saves from Roberto Soldado, Christian Eriksen, Paulinho and Gylfi Sigurdsson, and even when former Swansea man Sigurdsson did beat Marshall, he was denied by the crossbar.
But Paulinho finally broke the deadlock as he backheeled in Erik Lamela's pass from close range in the 92nd minute for his first league goal for the club.
"There could only be one winner," said Villas-Boas.
"We played so much football it would have been unfair to leave here with only one point.
"We got our reward in the end, but with the chances we created, if it wasn't for Marshall, it could have been a more comfortable game.
"You worry it can be one of those games. We played so open and sometimes on the counter they had a chance. But here, more than maybe any other game, we deserved the win.
"It's satisfying as I don't see many teams coming here and winning against a team who are well organised and well managed."
Cardiff felt they had twice come out on the wrong end of decisions by the officials.
The first came when Hugo Lloris appeared to handle outside his area as Fraizer Campbell attempted to round him, although replays suggested it was a very tight call.
The second saw Ben Turner's header from a corner chalked off after Aron Gunnarsson was adjudged to have impeded Lloris.
But Villas-Boas felt the officials had got it right on both counts.
He said: "I haven't seen it (the first incident), but I understand he was right on the limit. I'm not sure if there is some controversy there.
"Most people I have spoken to told me his hand is right on the line. I think if that is the case the referee made the right decision."
Of the disallowed goal, he added: "I think it was a foul for holding Hugo's arm. We spoke about it between us at half-time and he said he would have been fine if he had not been fouled."
Villas-Boas also confirmed Jermain Defoe's absence was down to a groin injury, with the striker due to undergo a scan on Monday.
While Danny Rose has a toe injury, although not a fracture, but should be available to meet Chelsea next weekend.
- Sports & Recreation