In what was Rene Meulensteen's first game in charge at Craven Cottage, Ashkan Dejagah gave the home side the lead, but Spurs turned the screw in the final quarter and earned their first league win since the end of October.
Meulensteen's side then came agonisingly close to levelling the London derby with the last kick of the game, but Pajtim Kasami's effort bounced off the post.
Defeat was harsh on the Cottagers, as they looked to be heading to victory before Chiriches' equaliser.
And there was nothing they could do about Holtby's stunning winner, with the midfielder picking up Kyle Walker's pass before unleashing an unstoppable drive into the top corner.
Though the result didn't go his way, Meulensteen will have been encouraged by his new players. All eyes are on the former Manchester United coach as he attempts to guide his new team away from the relegation places.
After the final whistle, the 49-year-old told BBC Sport: "I thought we were good and well organised. I said to the players I want an inspired performance, that is how we win the fans back, and we did that.
"Dimitar Berbatov was phenomenal, the way he led the line was evidence of his quality. No-one knows him better than me because I worked with him for a long time.
"I think we are hard done by with some results but it is up to the players, I refuse to get negative."
Andre: "We really needed to dig deep to find the strength to come back and we did it with fantastic strikes from Vlad and Lewis." #THFC— Tottenham Hotspur (@SpursOfficial) December 4, 2013