There was little to separate the teams after a 1-1 stalemate in 90 minutes on Tuesday night and there was no further goals in extra-time, then Ryan Esson produced a good stop from Darren Smith's penalty to end the Irn-Bru League Division Two side's hopes of an upset.
The visitors opened the scoring after 24 minutes when Billy McKay raced onto Richie Foran's through ball and lobbed the ball over Robbie Thomson.
Stenhousemuir were awarded a penalty five minutes before the break when David Raven chopped down Brown Ferguson and the striker got up to convert the resulting kick beyond Esson.
Driving wind and rain made for difficult conditions as the match got under way and both sides found retaining possession difficult during the opening exchanges.
The first chance of the match came for the home side when John Gemmell got a shot away under pressure from Gary Warren but could not find the target.
Thomson, making his debut after joining on loan from Celtic earlier in the day, was forced into his first save after 14 minute as he gathered Aaron Doran's fizzing effort at the second attempt.
As the rain began to subside Inverness began to find a foothold in the game and they broke the deadlock after 24 minutes when McKay raced onto Richie Foran's clever pass and lifted the ball over Thomson.
Doran again tested Thomson as the Clydesdale Bank Premier League side threatened to double their advantage.
Inverness were looking well in control of proceedings, however they handed their opponents a perfect opportunity to level when Raven felled Ferguson inside the area and referee Bobby Madden took little time in pointing to the spot.
Ferguson dusted himself off to take the resulting kick and held his nerve to leave Esson with no chance.
The equaliser clearly lifted the home players and they could have found themselves ahead on the stroke of half-time when Stewart Kean connected with Sean Dickson's cross leaving Esson rooted to the spot, unfortunately for the home side though the ball struck the top of the crossbar.
Andrew Shinnie's shot in the opening minutes of the second half was easily gathered by Thomson.
A wonderful piece of goalkeeping prevented Foran restoring Inverness' lead with 16 minutes remaining and the hosts passed up a good chance of their own two minutes later when Gemmell struck wide after good work by Smith.
Terry Butcher introduced Gavin Morrison in place of Conor Pepper but his side continued to find scoring opportunities limited.
They were however presented with a glorious opportunity with two minutes remaining, but Thomson again produced a superb save - denying Raven what looked to be a certain goal.
After enjoying an excellent first 90 minutes, Thomson in the home goal picked up where he left off in extra-time as he dived low to parry away Andrew Shinnie's skimming low shot.
Inverness went close again a minute later when Brown got in front of Graeme Shinnie's powerful strike to divert the ball away for a corner.
In the final minute of extra-time McKinlay was booked for a tired challenge on Josh Meekings, however the match headed to penalties after Inverness squandered the resulting free-kick.
Foran missed the opening penalty of the shoot-out and Bryan Hodge missed the hosts' third penalty to ensure parity after five penalties each.
Both sides netted their first sudden-death kicks but after Philip Roberts converted for Inverness, Esson denied Smith to ensure Butcher's side progressed.