"It was very important for the team, for both teams. (We knew) a win today would be a big boost of confidence and it fell our way," Villas-Boas told a news conference.
"We went down a goal at the moment when we looked more composed and more in control and then we had to dig deep to find the winning goals. Two moments of inspiration settled the game."
The hosts took the lead through Ashkan Dejagah just before the hour after a defence-splitting pass from the unsettled Dimitar Berbatov, who was booed before kickoff after his agent said earlier on Wednesday that he wanted to leave the club.
The victory moved Spurs up to sixth in the Premier League, while Fulham remain in the relegation zone with 10 points from 14 matches.
Until Chiriches struck, the west London club seemed headed for victory in their first game under head coach Rene Meulensteen after the five straight defeats which led to the sacking of fellow Dutchman Martin Jol on Sunday.
There seemed little danger when Fulham cleared a corner but the Romanian struck a low left-foot drive from 35 metres that flew into the corner of Maarten Stekelenburg's net in the 73rd minute.
A relieved Villas-Boas clenched his fists in the air to celebrate the goal, having endured a torrid time at the hands of the media since Tottenham's 6-0 defeat at Manchester City last month.
He had more to enjoy almost 10 minutes later when Holtby, who he brought on for the ineffective Etienne Capoue at halftime, cut inside and unleashed a fierce drive from just outside the penalty area to seal the points.
Meulensteen said the defeat was "very hard to take" but added that he would use all the experience he gained as assistant to Alex Ferguson at Manchester United to keep Fulham up and said he was "absolutely" sure they would survive.
"Fulham are going through a tough time everybody knows that. I wanted an inspired performance and from a tactical point of view a disciplined performance and we got that," the Dutchman told reporters.
"I have been fortunate to sit alongside the most successful manager Alex Ferguson.
"He said in life as well as in football you have to face up to challenges and sometimes you are faced with adversity.
"The most important thing is to embrace the challenge and face it head on and that's what we"re trying to do."