John O'Shea's own goal sealed a second successive victory for Spurs on the back of their 2-2 draw with Manchester United, a run which has gone a long way towards erasing the memories of their 6-0 horror show at Manchester City last month.
Villas-Boas, who found himself under pressure in the wake of that demolition job at the Etihad Stadium, said: "It was a very important win for us. It completes a good, good week, a good start to December.
"Two away fixtures, a Premier League midweek fixture and Manchester United at home was always a difficult scenario following our defeat against City, so it's a great fightback from the team finally completed - and we have put ourselves back on track in a position where we can challenge for the top.
"Credit to the players. Our group has been immense in this situation that we faced and fought back to these great results recently."
The victory, which followed Wednesday night's 2-1 win at Fulham, left Spurs in sixth place in the table, but only three points behind second-placed Liverpool, who head for White Hart Lane next Sunday.
Villas-Boas, who is targeting a Champions league berth, said: "It's very tight. Now we have Liverpool at home and Southampton away, teams that are in the frame with us.
"It's important for us, if we want to get ourselves near the top, to have a result against Liverpool, so this enables us to be in touching distance with them, and hopefully we can do just that on Sunday against them."
After a quiet start to the game, Sunderland took the lead when Spurs goalkeeper Hugo Lloris misjudged Ondrej Celustka's cross and could only punch it to Adam Johnson, who gleefully slammed it into the top corner.
But their joy was short-lived and Tottenham were level within six minutes when the impressive Paulinho turned Nacer Chadli's header back across goal past keeper Vito Mannone.
The game was won five minutes after the restart when the luckless O'Shea saw Moussa Dembele's driven cross clip off him and fly past Mannone, the fifth own goal Gus Poyet's side has scored this season.
Spurs had more than enough opportunities to kill the game off, but could take none of them with Jermain Defoe twice hitting the post, and they might have been made to pay when Sebastian Larsson's 75th-minute corner appeared to be blocked by substitute Sandro's arm, although referee Lee Mason was unmoved.
Villas-Boas said: "I haven't seen the incident, but everybody has confirmed that it's a penalty, so it's difficult for Gus to accept it because he is in need of points.
"But if we had finished our situations, that penalty wouldn't have made a difference, I think there was something there."
A downbeat Poyet refused to use that decision as an excuse, however.
He said: "I don't know what to say. I'm running out of words. I'm trying to be as honest as I can, but sometimes it doesn't matter.
"I don't like it, I don't enjoy it. I hate losing, hate it, and I don't remember losing too many games like that. It hurts, I can tell you that.
"The next four games are massive, absolutely massive. Me, I'll keep going. I'm not going to give up, I can promise you that."
Poyet also refused to accept that the rash of own goals his team has conceded was purely down to bad luck.
He said: "One, two, three - back luck. Five? Too many. Me, I believe in coincidence once, twice. Five? No, I don't.
"Somehow always something happens. Who is going to be next? Do you know? Let me know so I don't play him."