Villas-Boas' position as Tottenham manager came under scrutiny following last week's 6-0 defeat at Manchester City, but the Portuguese tasted victory again on Thursday in Tromso.
Vlad Chiriches and Mousa Dembele scored their first goals of the season to give Spurs a 2-0 win that guaranteed them top spot in their Europa League group with one match to spare.
Spurs struggled to find their rhythm in the first half and they took over an hour to beat Tromso stopper Benny Lekstrom, but Villas-Boas was delighted that his team overcame a tricky hurdle in the freezing temperatures of northern Norway.
"I am very happy for the players to have bounced back from the defeat against Man City," the Spurs boss said.
"Obviously the opponent we have on Sunday is the biggest that we can have.
"But to prepare for that game, it was important to get back to winning ways tonight 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."
Chiriches turned home Gylfi Sigurdsson's free-kick in the 63rd minute - although the ball was helped over the line by Tromso's Adnan Causevic - and Dembele then wrapped the win up with 15 minutes left.
Roberto Soldado drew a blank once again and Nacer Chadli missed a sitter, but in truth it was a case of job well done considering the conditions the team had to play in.
Temperatures dropped below zero and the players had to endure heavy snowfall during the first 10 minutes of the match, which had to be played on an artificial surface due to the conditions in Tromso - which is so far north that it shares the same latitude as Alaska and Siberia.
"The players adapted to the conditions quite well," Villas-Boas added.
"The quality of the pitch was fantastic. We came through okay with no injury worries. The conditions were tricky with the first blizzard of snow, but after that it settled down."
Speculation mounted that Villas-Boas could be on his way out of White Hart Lane following the hammering at the Etihad Stadium.
Another defeat to City's neighbours would pile more pressure on the Portuguese, and unfortunately for him, he will face a United team with their tails up following their 5-0 win in Leverkusen on Wednesday night.
Villas-Boas had the luxury of taking in that game in Tromso's five-star Radisson Blu hotel. On Sunday he will cut a much more tense figure on the touchline, but he says his men are ready to take on David Moyes' squad.
"I watched the game last night. It was a good performance but it will have no bearing on Sunday," he said.
"They are on a good run that changed their fortunes. We don't expect an easy match, but it will be a completely different story (for United) on Sunday. I'm not being disrespectful, but it will be a different game in different conditions and our players will be mentally ready."
Villas-Boas' critics multiplied last weekend after the rout at City.
Jamie Carragher, Gary Neville and Alan Shearer all laid into the Tottenham team for their poor showing in the north-west, and another critic came out of the woodwork on Wednesday in the form of Lord Sugar.
The former Tottenham chairman aired his concerns about Villas-Boas' management on national radio and said his dream scenario would be to see the Portuguese replaced by former United boss Sir Alex Ferguson.
Villas-Boas, in a far better mood than during his cagey pre-match press conference, joked that Sugar had a point.
"I think it is pretty fair (to say Ferguson could do better)," the 36-year-old said with a big smile.
"With the record Ferguson has, he would be a pretty good manager in any club in the world."
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