First-half goals in the space of two minutes from Gareth Bale - his 20th of an outstanding campaign - and Aaron Lennon just before the break proved enough to hold off the Gunners, who had started the game well and rallied after Per Mertesacker's header on 51 minutes, but failed to find an equaliser.
Spurs moved back above Chelsea up into third place in the Premier League, and crucially opened up a seven-point gap on Arsenal - who now look in real danger of failing to qualify for Europe's premier club competition for the first time in 16 seasons.
While not getting carried away with the win, Villas-Boas believes it will have a huge psychological impact on Arsene Wenger's team.
"Obviously it doesn't mean nothing because last year when Arsenal won to shorten the gap to seven points it felt that everything was too possible for Tottenham's qualification and it shifted very, very quickly, so it is not a big margin yet for us to be completely safe," the former Chelsea manager said.
"What we think is it can have a direct effect on their motivation - on ours too, obviously. But particularly on them because the difference from last year is we are on an upward spiral in terms of confidence and they are in a negative spiral in terms of results - and to be out of that negative spiral is extremely difficult."
Arsene Wenger, meanwhile, admitted Arsenal now face a "massive" task to get back into the top four, but insisted they are not about to throw in the towel.
"It is frustrating because we put so much effort in and lost the game when we were on top," said Arsenal boss Wenger. "We were 2-0 down when we should have been 2-0 up.
"After, it gave them confidence to defend well, which is what they did for the rest of the game.
"It is difficult to understand how you lose a game like that.
"We had a great attitude and came out with no points because we were not efficient where it matters - at the front and in the back."
Wenger added: "It will be a massive challenge. I said before the game that we could not afford to drop points.
"It happened to us many times this season and only in big games. It's difficult to say why - there's no common thing. In all the games there is a different problem, but after you make it difficult for yourself.
"I cannot fault the attitude or the effort that the team produced, or the spirit the team has shown, but you give yourself a mountain to climb every time in a game of that magnitude."