Vlad Chiriches and Lewis Holtby produced fine strikes from outside the box to help Spurs crawl past Fulham 2-1 in the Barclays Premier League at Craven Cottage.
Fulham led through Ashkan Dejagah's first goal for the club, on Rene Meulensteen's debut in sole charge following Martin Jol's departure.
Tottenham struggled to control the game, especially in midfield, but Villas-Boas said sometimes snapshot quality can be enough.
Now the Portuguese boss wants Spurs to complete the process of bouncing back from their lean November, after rising to sixth in the league standings.
Villas-Boas believes victory at Sunderland's Stadium of Light will drag his side back into the race for a Champions League spot.
He said: "At the moment it's going well for us, I think we managed to get two good wins and a good draw against Man United.
"So to complete the bounce-back, if we can say that, it would be great to win at Sunderland.
"To do that after a midweek Premier League fixture and after a good draw against Man Utd, that would show we really are alive.
"Some surprising results today help us come up a couple of places up the league table.
"And now a couple of wins could bring us back into the frame for the top four.
"We have to do it more often now, when teams drop back, to have a go from outside the box.
"This time it worked.
"We had lots of shots against a side like Newcastle but couldn't break them.
"This time we were fortunate that they ended up in the back of the net."
Villas-Boas confirmed Jan Vertonghen rolled his ankle, leaving him a doubt for the Wearside trip, while Moussa Dembele's ongoing hip complaint led him to withdraw from the Fulham match at short notice.
Defender Danny Rose will make a return to training on Thursday, but Villas-Boas does not expect him fully fit for 10 days.
Fulham's new boss Meulensteen hailed unsettled strike Dimitar Berbatov's all-round contribution as "unbelievable".
Berbatov laid on the goal for Dejagah and forced Lloris into a late save.
His agent has confirmed he is "not happy" at Craven Cottage and will seek a move in January, but Meulensteen said it is time to focus on the busy Christmas schedule.
Confident Berbatov can still boost Fulham's Premier League survival fight, Meulensteen said: "If he performs the way he did tonight.
"I thought he was fantastic.
"He was unbelievable, he led the line fantastically, and I know really, really well what Dimitar is capable of doing because I've worked with him for so long.
"The most important thing is that we have to focus now from game to game, right up until the start of January.
"I've had some good chats with Dimitar, he's a player who really cares for this club and I thought that was evident the way he performed."
Meulensteen suggested Spurs keeper Lloris kept his side in the match, making two crucial late saves.
He said: "It is very, very, very hard to take.
"Fulham are going through a tough time, everyone knows that.
"It was an inspired performance, and from a tactical point of view it was a disciplined performance.
"That first goal from Tottenham fell out of the sky really.
"It was a good strike, but that's hard to take.
"I thought Lloris pulled off a couple of 'worldy' saves."