Inverness were relegated from the Scottish Premier League following a narrow home defeat to Falkirk om Saturday.
Substitute Michael Higdon turned home Jackie McNamara's inviting cross after 68 minutes to ensure the Bairns remained in the top-flight.
The turning point of the match came after 39 minutes when Ross Tokely was sent off for a last-man challenge on Steve Lovell.
Richie Foran should have given Inverness the lead in a tense first half but was denied by an excellent stop by Dani Mallo.
The result means Terry Butcher's side will be playing First Division football next season.
Inverness made one change to the side that lost 1-0 to Kilmarnock last weekend with Latvian defender Pavels Mihadjuks replacing David Proctor.
The Bairns made four changes with Gerard Aafjes coming in for defender Steven Pressley who missed out after losing his appeal against last week's red card against St Mirren.
Full back Jackie McNamara returned to the side at the expense of Lee Bullen, while Patrick Cregg and Carl Finnigan also started with Neil McCann and Higdon dropping to the bench.
With so much at stake it was, as expected, a nervy and tentative start from both sides. The home side made the first foray forward when Foran latched onto a Filipe Morais flick-on before darting past Aafjes and unleashing a low drive that was comfortably gathered by Mallo in the Falkirk goal.
The Bairns had a chance to test the Caley rearguard after 11 minutes through a Burton O'Brien free-kick from a promising position but French defender Lionel Djebi-Zadi headed the ball to safety.
Foran then spurned a great chance to put his side ahead after 12 minutes when a Morais cut-back fell kindly into his path but the Irish striker's close-range shot was clawed away brilliantly by Mallo.
Morais flashed a powerful shot inches over Mallo's crossbar as the home side enjoyed a period of dominance.
Falkirk appeared to have survived the early Caley onslaught and could have broken the deadlock after 29 minutes through Lovell but the striker dwelled on the ball too long at the vital moment and his weak shot was blocked by Djebi-Zadi.
The talking point of the half came after 39 minutes when the home side were reduced to 10 men when Tokely was sent off for a last man challenge on Lovell.
Butcher brought on Russell Duncan for McBain after 42 minutes to shore up his defence until half-time.
Despite their numerical disadvantage, Inverness made the better start to the second half and Bairns striker Finnigan breathed a sigh of relief when his defensive header from an Ian Black free-kick went over his own crossbar.
Falkirk manager John Hughes made his first change after 53 minutes withdrawing Arnau Riera, who was having a quiet game, and bringing on Mark Stewart.
And the substitute almost made an immediate impact when he lobbed Michael Fraser with a first-time volley but the retreating Duncan headed the ball off the line to safety.
Inverness were sitting deeper and deeper in their own half and Higdon was introduced for Lovell after 65 minutes in attempt to prise open the stubborn home defence.
And this change did make the difference. McNamara exploded down the right and played a pin-point cross into the path of Higdon and the substitute prodded the ball past the helpless Fraser to the delight of the vocal travelling support.
The visitors sensed blood and pressed for a second with Cregg unfortunate to see his curling effort fall the wrong side of the post.
Eric Odhiambo was then brought for the tiring Morais with 15 minutes remaining as the home side fought to stay in the top flight.
The Englishman had a weak effort cleared from a Black free-kick before Brian Kerr dragged a volley wide with the Inverness supporters beginning to fear the worst.
As a final throw of the dice Andy Barrowman was brought on for Black who was making his last appearance for Caley before his summer move to Hearts.
The visitors should have wrapped up all three points when Stewart centred the ball for Finnigan but the striker blasted over from six yards with the goal gaping.
In the dying stages Kerr shot over before Duncan was denied by Mallo but the Highlanders could not find the goal to secure their top-flight status.