Spurs have struggled to find any kind of consistency in the league this season, leading to widespread criticism of the Portuguese boss who spent close to £100million during the summer.
However, after falling behind to Ashkan Dejagah's goal, Vlad Chiriches and Lewis Holtby both got on the scoresheet to secure the victory.
The win makes the table look slightly more respectable for the north London club, who move from ninth to sixth and now sit just three points adrift of Liverpool and Everton, who lie fourth and fifth respectively.
Villas-Boas said: "We have been waiting a long time for this win, it was important to finish the job and get the win.
"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 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."