The Portuguese tactician expressed his relief at Paulinho's 93rd-minute goal but insisted the three points were well-deserved after the pressure they had put Cardiff City under
The visitors spent most of the game on the front foot and were only kept at bay by a string of saves from Cardiff goalkeeper David Marshall.
However, Paulinho back-heeled a 93rd-minute winner after latching onto Erik Lamela drilled pass across the six-yard bow, and Villas-Boas feels Spurs' dominance throughout warranted all three points.
"Today it was different from normal in that there was justice in football," he told reporters. "We created so many chances that there could only be one winner."
"Marshall is a great goalkeeper. He did extremely well today."
Villas-Boas feels the manner of the victory will provide his squad confidence as they aim to continue their impressive away form of last season.
"Last season we had the best record away from home after Manchester United," he continued. "We looked very strong.
"Bearing in mind the win [Cardiff] got against Manchester City there won't be many teams getting points here so I'm happy. It's a great win. But I suffered a lot … like everyone else!"