The former Monaco defender came back to haunt his old side as he held his nerve from 12 yards to book a final clash with Paris Saint-Germain, the side they faced in their last final appearance in 1995.
After 120 goalless and dull minutes at Stade Louis II, the shootout finally provided some excitement with the two sides trading blows, before Nabil Dirar crashed his effort against the crossbar.
That left Squillaci – Bastia's ninth penalty taker – the chance to seal victory and he made no mistake in beating Maarten Stekelenburg.
The thrilling nature of the shootout was a surprise after a match devoid of any real excitement, with Dimitar Berbatov and Julian Palmieri - for Monaco and Bastia respectively - wasting the best openings.
It mattered little, though, as the Corsican side dumped their hosts out, and booked their spot in the showpiece.
Leonardo Jardim welcomed back Ricardo Carvalho to the heart of his defence as one of five Monaco changes, and the Portuguese veteran was needed as Bastia made a bright start.
Ryad Boudebouz led the visitor's charge with several dangerous runs in the attacking third, but Carvalho marshalled the Monaco back line well to ensure Stekelenburg was not called into action.
Chances were few and far between but Monaco were able to find a gap in Bastia's defence after 22 minutes.
Valere Germain was unable to get the ball out of his feet, though, having been played in by Bernardo Silva, and despite the loose ball falling to Berbatov, he could only shoot at Bastia goalkeeper Alphonse Areola from 15 yards.
A half devoid of quality should have had its opening goal three minutes before the break as Giovanni Sio raced past Carvalho, but his first effort was well saved by Stekelenburg before the Bastia debutant wasted the rebound.
With a place in the final up for grabs, the intensity was always likely to improve in the second half and Moutinho should have been more accurate from 20 yards once play resumed.
Anthony Martial's mazy run into the penalty area failed to produce an effort on goal, however the hosts worked the ball back to Moutinho, only for the Portugal international to fail to work Areola from distance.
Again both sides struggled to create in the final third, with more than 15 minutes passing before the game's next notable chance - which saw Elderson Echiejile head straight at Areola at the back post.
While Monaco were largely in control, Bastia offered a reminder of their threat when Boudebouz created a shooting chance for Squillaci, but the defender fired just wide.
Boudebouz was beginning to be more involved and in the 82nd minute, a cross from the Algeria international was met by Palmieri - only for his diving header to be straight at Stekelenburg.
Extra time failed to produce an increase in quality, with only Hervin Ongenda going close in the first period, the forward skewing his shot wide from inside the penalty area.
Both sides missed their second attempts in the shootout, and Moutinho threw away Monaco's chance to win after Sio's effort had been easily saved.
The score moved on to 6-6 before Dirar saw his effort thud off the crossbar, leaving Squillaci to score the winner and put Bastia in the final.
