They had to come from behind at Craven Cottage too, after Ashkan Dejagah fired the hosts ahead after 57 minutes, latching on to Dimitar Berbatov's through-ball and firing low past Hugo Lloris.
Berbatov was one of Fulham's star performers, just hours after his agent revealed that the striker would favour a move away in January.
Spurs laboured in their response, with Jermain Defoe leading the line as Villas-Boas benched summer signing Roberto Soldado in an attempt to return to winning ways in the Premier League.
Their equaliser came from the least likely of sources, as Vlad Chiriches bagged his first goal for the club after 72 minutes, smashing home a low half-volley from 30 yards out.
There was a touch of fortune about the goal too, as Defoe looked to be in an offside position before jumping over the ball as it made its way in off the near post.
Holtby completed Spurs' comeback with another stunning effort with just five minutes remaining.
The German, brought on as a second-half substitute, cut inside and unleashed an unstoppable effort past Maarten Stekelenburg, scoring his first Premier League goal in the process.
In Rene Meulensteen's first game in charge of Fulham, they came out of the blocks firing as Berbatov starred in a lone striker role against his former club.
Defoe had the first opportunity on goal after seven minutes however, with his low effort stinging the palms of Stekelenburg.
The closest the home side came to a real chance was from Pajtim Kasami's early through-ball to Berbatov.
The Bulgaria striker looked well-placed to control and sneak through for a one-on-one with Spurs goalkeeper Lloris.
But his first touch let him down at the crucial moment, and the half-chance evaporated on the icy autumn air.
After that it was Spurs' chance to turn wasteful once again.
Defoe cut clear on the left after a deep clearance, held up play well, and waited for Erik Lamela's well-timed delayed run into the box.
The former West Ham striker's cut-back begged for a finish; instead Lamela side-footed wide.
Lamela was once again in action with a rising drive from the area's edge, but Stekelenburg was easily equal to the challenge.
Alexander Kacaniklic shone from Fulham's midfield, while Giorgios Karagounis also tested Lloris from range in an end-to-end first half.
Paulinho spurned the best chance however, having been played in by Defoe on the break, but, after evading two challenges in the area, he skewed his effort high and wide from eight yards.
The second half followed much the same pattern, but opened up further when Dejagah fired low and hard past Lloris when played in by a sumptuous Berbatov ball.
Meulensteen's men were unable to hold out though, with Chiriches firing in with a first-time strike after a loose headed clearance from a Fulham corner.
Just as Fulham looked to settle, Spurs struck again, Holtby smashing in another good finish, to floor the hosts.
Fulham pressed again at the death, but Berbatov clipped wide before Kasami struck the outside of a post with the final play, though Lloris was primed to save an on-target shot.