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 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 today, 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.
Source: PA
Source: PA