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 Barclays 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 Sunday's 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."
Tottenham are now within striking distance of second-placed Manchester City, ahead of their game against strugglers Aston Villa on Monday night.
Villas-Boas, however, is determined to hold a sense of perspective.
"At the moment we keep our feet on ground. We still have some difficult games to play against big teams - Liverpool, Chelsea and Manchester City plus Everton - teams who have same objectives as ours, so it hasn't finished yet. Everything is still possible and we just have to gather the most amount of points that we can.
"There is a great focus on trying to make this year the year we qualify for the Champions League once again. Everybody is bonding together regarding our objective.
"The players are our main reference as they have been absolutely outstanding. They make it public - they want to be in it. Their desire has been tremendous in these recent games."
Villas-Boas added: "Everybody's ambition to be there. The club could be propelled into a big club in England in the future."
After soaking up plenty of Arsenal pressure, the home side capitalised on some poor defensive lapses by the visitors as first Bale and then Lennon cut through a static back line.
"It's part of players' talent and ability to recognise where spaces are. Obviously we prepared our game, looked for those gaps in behind. The players have feeling for what they are doing - they are able to put the ball through and able to score."
Spurs defender Michael Dawson was delighted with his side's win and described the three points won as "massive".
"It's massive to go seven points clear, in a north London derby, to get three points is massive but we have a long way to go, but it is a good day," Dawson said.
"We have a great squad and we showed that today [Sunday].
"It probably wasn't our best performance. We didn't keep the ball like we know we can but showed great determination and we got the three points we deserved.
"We want to be back in the Champions League. I think we showed that in the celebrations after. The fans will go home happy and have the bragging rights at work tomorrow [Monday]."