Goals from Jan Vertonghen, Gareth Bale and Clint Dempsey saw Spurs to their first victory at Old Trafford in 23 years and their first win over Sir Alex Ferguson's team in 27 attempts a run dating back to May 2001.
After a slow start to Villas-Boas' reign at White Hart Lane, three straight league wins have taken Spurs into fifth place and seem to have turned the tide for their Portuguese manager.
"We were tremendous today," said Villas-Boas after Saturday's thrilling success. "The players really put in the effort, the desire, the intensity from the beginning.
"When you see a team with so much desire to hold onto a historic result, you can count on each other to do big things this year. That's the most important thing, the most important lesson we take out of tonight.
"The players really felt they could nick a win here and the first and second half is an expression of that desire and ambition, though in different ways.
"In the first half, we attacked and kept the ball. In the second, we defended," added Villas-Boas, still only 34.
"This is a very very special night for us," added Villas-Boas, who was sacked by Chelsea before Spurs' London rivals won the Champions League last season.
"It must serve as an example to us for what we want to achieve in the future. In the end it is just an important three points that will hopefully serve as an inspiration for the future."
Villas-Boas reserved special praise for man-of-the-match Bale, after revealing the Wales winger had only managed to train for one day in the week leading up to Saturday's clash due to illness.
"He trained only one day during the week and is still with a sore throat and fever," said Villas-Boas.
"We had problems with (Gylfi) Sigurdsson as well, who had diarrhoea and vomiting."
The defeat, United's first home reverse of the new campaign, left them four points behind leaders Chelsea and would have caught the eye of those clubs competing to wrest the league title from Manchester City's grasp.
But the Tottenham manager does not believe his side is one of them.
"Our quest is to qualify for the Champions League. It is very difficult to go for the title," said Villas-Boas.
"We understand it is a place where the great teams of this country belong. We want to win a trophy this season. We want Champions League qualification."
United manager Ferguson was left to rue at least two rejected penalty claims, with the best a clear two-handed grab by Vertonghen on Nani in the first half.
However, referee Chris Foy decided the winger had made a meal of the foul -- and for once Ferguson agreed with an official.
"I think there were quite a few penalties," he said. "The one in the first half was a clear penalty kick, but maybe Nani made a meal of it. He didn't need to do that."
Ferguson brought fit-gain Wayne Rooney off the bench at half-time him and the England striker responded by setting up Nani for United's first goal.
Shinji Kagawa pulled back a second for the Red Devils, after Dempsey had made it 3-1, and Ferguson hinted strongly it had taken a blast of his infamous 'hairdryer' during the interval to get the desired change.
"I think the attitude changed and that's the most important thing," said Ferguson.
"Wayne's ability does help too, but the attitude of the players was absolutely brilliant, everywhere on the pitch.
"Their attitude to winning was great. They got stuck in. They started going to win the ball rather than standing off as they had in the first half. That was the main difference.
"We should have dealt with it better after scoring, but there are a 100 ways to look at losing a goal.
"You analyse it, but it was a bad break after getting one back. If we had kept it that way for a few minutes, I think we'd have won the match."