The Portuguese has come under pressure of late after Tottenham's slump in form, which culminated in a disastrous 6-0 Premier League loss to Manchester City last weekend.
However, Tottenham responded in fine style from their European excursion to Norway on Thursday, beating Tromso 2-0 on their way to topping Group K.
An own goal from Tromso defender Adnan Causevic along with a second for Mousa Dembele gave the Londoners the win.
Tottenham will host United when they return to domestic action on Sunday, having slipped to ninth in the table after back-to-back league defeats against Newcastle United and City either side of the international break.
And Villas-Boas admits that it was important to get back to winning ways quickly ahead of that clash.
"Obviously the opponent we have on Sunday is the biggest that we can have," he said.
"But to prepare for that game, it was important to get back to winning ways here, and we did it in a fashion where we looked solid and created lots of chances.
"I am extremely happy with the performance and result."
Alexia Putellas: "We’re already the only club to have won the men’s and women’s Champions League, so the only thing even more historic to do than that would be to win it in the same season"
‘Trent has won everything he can for Liverpool, but of those who’ve left that we wanted to stay, who’s actually done better? I can only come up with one’: Reds legend highlights potential danger of Alexander-Arnold moving to Real Madrid
