Falkirk advanced to the CIS Insurance Cup quarter-finals for the first time since 1994 courtesy of Anthony Stokes' 60th-minute strike.
Teenager Stokes was the match-winner for Falkirk
The 18-year-old striker, on-loan from Arsenal, brought a dull game to life with a wonderful goal.
The Irish youngster skipped past three tame challenges before lashing a powerful strike past keeper Mark Brown.
Earlier, Stokes fired just wide and the Bairns' Mark Twaddle had a shot headed off the goal-line by Russell Duncan.
The game was far from a classic but the visitors were the more positive side and, in Stokes, they have a player who looks capable of turning matches.
After a dull opening period, the lively Stokes saw his tame effort at goal comfortably gathered by Caley Thistle goalkeeper Mark Brown but later curled a shot just over the crossbar.
Falkirk continued to create the better chances and were unfortunate not to take the lead when Duncan headed a shot fromTwaddle off the goal-line midway through the first-half.
Inverness grew stronger closer to the break though and Craig Dargo went close with a dipping shot after good work on the edge of the visitors' penalty area.
Falkirk took the lead on the hour when Stokes bundled his way past a trio of Inverness defenders before blasting a close-range shot past the helpless Brown.
The home side attempted to respond to that setback immediately and Liam Keogh sent a snap-shot on the half-volley fizzing just past the post.
Inverness head coach Charlie Christie threw caution to the wind and withdrew left-back Richard Hastings for striker Rory McAllister.
That substitution nearly paid dividends in the 66th minute when McAllister managed to make contact with Barry Wilson's cross at the back post, but the teenager could only place an effort into the side-netting.
Two minutes into stoppage time, Inverness striker Graham Bayne went close with a diving header which went just over.
But Falkirk's goal remained unbreached allowing the Bairns to deservedly move into the last eight.
Inverness CT: Brown, Tokely, Dods, Munro, Hastings (McAllister 73), Wilson, Duncan (Morgan 62), Keogh, McBain, Dargo (Hart 80), Bayne. Subs Not Used: Fraser, McCaffrey.
Booked: Munro, Dods, Hastings.
Falkirk: Higgins, Barr, Dodd, Milne, Ross, Thomson, Cregg, O'Donnell (Craig 19), Twaddle, Stokes (Moutinho 74), Gow. Subs Not Used: Lambers, Latapy, Scobbie.
Booked: Cregg. Goal: Stokes 60.
Ref: D McDonald