Spurs came into the game without a win in four league encounters, and seemed in dire straits as Ashkan Dejagah got the Rene Meulensteen era at Craven Cottage off to a great start with a 57th-minute opener.
However, Vlad Chiriches' thunderbolt and a Lewis Holtby winner turned the tables and eased the pressure on Villas-Boas, whose job security has come under scrutiny in the media, leading to a backlash from the Portuguese.
The win moves Spurs from ninth to sixth in the table and they are now three points behind Liverpool and Everton, who sit in fourth and fifth respectively.
"We have been waiting a long time for this win, it was important to finish the job and get the win," he told Sky Sports.
"It puts us back on track and (we) jump a couple of positions in the table, it's another away win which is important.
"It was very important, (their) goal came in a good period for us. But it was end-to end stuff, not a lot of control but it was frenetic.
"To keep in touch with people at the top was important, especially after some surprising results this evening.
"It was important for us to be in there among the top teams to take our challenge through. December and January are very important months in the Premier League."
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