Higdon's eighth goal of the season secured Falkirk's SPL status
Inverness were relegated from the Scottish Premier League after substitute Michael Higdon scored as Falkirk won to stay in the top flight.
Caley Thistle started brightly and Bairns goalkeeper Dani Mallo made a wonderful save to deny Richie Foran.
The hosts were reduced to 10 men when Ross Tokely was sent off for a professional foul on Steve Lovell.
Falkirk wore their hosts down and Higdon scored from close range on 68 minutes from Jackie McNamara's pass.
Trailing the host by two points, Falkirk needed to win to stay in the league, while Inverness needed only a point.
And, after a nervy opening period, Inverness looked eager to get the goal that would give them a massive advantage.
The home side's Foran made Mallo save when he shot low from 15 yards before the Falkirk goalkeeper made an astonishing save to keep his team level with 11 minutes gone.
Felipe Morais made for the bye-line, cut the ball back to Foran and the Irishman hit a powerful shot from eight yards that Mallo superbly palmed away.
Morais was involved in most of the home side's early attacks and, with the visitors backing off, the Portuguese had a strike from distance that went just over.
Falkirk had posed little threat, but before the half-hour mark Scott Arfield threaded a neat ball through to Lovell, the Bairns top-scorer hesitated when he should have shot and the chance was lost.
But, shortly before half-time, Inverness were dealt a massive blow when they were reduced to 10 men.
With Lovell going for a ball over the Caley Thistle defence, last man Tokely climbed over the striker as he tried to recover ground.
Tokely was almost in tears after his dismissal
Lovell was downed on the edge of the box and, after a nod from his assistant, referee Eddie Smith brandished the red card to the Inverness' longest-serving player.
Despite their extra player advantage, Falkirk found themselves hemmed in their own half after the restart and there was a nervy moment when Carl Finnigan headed just over his own bar.
But they soon picked up their game and substitute Mark Stewart lobbed high over on-rushing Caley Thistle keeper Michael Fraser, but the ball was headed away from the goal to safety.
The visitors had the 10 men camped in their own half but struggled to create any scoring opportunities.
However, Bairns boss John Hughes swapped Lovell for Higdon up front and the English striker was to have a crucial contribution.
Within five minutes of coming on, Higdon met McNamara's ball across goal to divert it past Fraser from six yards and give them a vital advantage in the SPL survival fight.
Finnigan blazed an easy chance for the Bairns' over the bar with five minutes to go and Brian Kerr, Russell Duncan and Dougie Imrie all spurned chances for the hosts in the closing minutes.
But Falkirk held firm and the final whistle was greeted with scenes of jubilation from the away side - and dejection for Inverness, who will play in the Scottish First Division next season after five years in the top-flight.
Inverness manager Terry Butcher: "To lose in the manner we did in the last game is hard to take.
"I feel so sorry for the fans, players and everyone at the club because they've given everything today.
"Everything was going according to plan and then all of a sudden the red card comes out of nothing.
"I've only seen it once, but I thought there was doubt about it being a clear goalscoring opportunity.
"Although it's hard to look beyond this afternoon, the work starts now in bouncing back next year."
Falkirk manager John Hughes: "I'm just delighted for the players as they've been through the mire this year.
"We're thankful to get a second opportunity after last week and we've taken it by coming up here and winning.
"But it feels like we've won it by default against 10 men. I had a go at them at half-time. We got our reward.
"What a fantastic season it's been: staying in the SPL, semi-final of the CIS Cup and a Scottish Cup final to look forward to. It's not too bad."
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