Vertonghen opened the scoring with a neat finish after good work from Gareth Bale, and then turned provider for the Welshman to double Spurs' lead.
"Jan did it so well for Ajax, and now is doing it for us," said Villas-Boas.
"It's great to see, and he gives us something else."
The Portuguese boss admitted his relief at the result, which was made more difficult after a spirited second-half fightback from the home side.
"It was an important victory after back-to-back defeats," he added.
"We cannot expect to dominate away from home, but we had a couple of chances to make it three which would have helped us.
"Momentum shifts quickly, but we just have to keep winning."