Having fallen behind in the London derby to Ashkan Dejagah's great second-half effort, the pressure looked set to pile further on an under-fire Villas-Boas after an indifferent start to the season.
Two stunning late goals from first Vlad Chiriches and then Lewis Holtby left the hosts reeling however, and gave Spurs a first league win since beating Hull City at the end of October.
On the long-awaited victory, Villas-Boas told Sky Sports: "We've been waiting a lot for this win.
"It was important to conclude the job, so it gives us that winning feeling, finally.
"It puts us back on track, we jump a couple of positions in the table."
Despite their dominance, Spurs fell behind when Dejagah fired home from Dimitar Berbatov's through-ball.
"We were a bit unlucky to suffer that goal because it was probably our best moment," Villas-Boas said. "We looked in control.
"After the goal the game reflected the first half; either team could have scored. It was very frenetic with not a lot of control."
Excellent strikes from Chiriches and Holtby saved Spurs however and gave them a much-needed win, but Villas-Boas reserved special praise for his match-winner.
"Great strike. Both were great strikes, and Lewis always comes in with a positive attitude. He brings his desire and ambition into the game."
After triumphing over Fulham in Rene Meulensteen's first game in charge, Villas-Boas looked ahead to rekindling Spurs' European hopes.
"It's always difficult against a team with a change of manager, but we have to build on this win. We need to put our challenge back on track for the Champions League places."
One blot on Spurs' victory will be an injury picked up by Jan Vertonghen late on.
With Danny Rose already indefinitely sidelined, Villas-Boas will have grimaced as Vertonghen, who has been filling in at left-back, hobbled off at the full-time whistle.
"It's his right ankle. We have to assess it but it looks quite swollen. Hopefully it's not serious."
Spurs now face Sunderland, who were valiant in falling 4-3 at home to Chelsea on Wednesday. Despite talking up his opponents, Villas-Boas will surely head into the game with big prospects for his resurgent Spurs side.
"They're not afraid to play big teams. Gus Poyet is a manager who likes his teams to play football, so hopefully it'll be an entertaining game."