With so much at stake, the tension was palpable, but it was Caley Thistle who settled the best early on.
Only five minutes had gone when Filipe Morais' flick on sent Richie Foran racing on goal only for his low drive from the angle to be held by Bairns goalkeeper Dani Mallo.
The pair then combined to set up the best chance of the game on 12 minutes. Morais cut the ball back perfectly into the path of Foran seven yards out, but his well-struck shot was superbly saved by Mallo, who parried his effort away to safety.
Portuguese-born forward Morais was at the centre of all Caley Thistle's best attacks and he had Mallo worried again with an ambitious effort from the angle that only just cleared the crossbar.
Falkirk had rarely threatened, but their hopes of gaining the win they needed to secure safety were boosted seven minutes before the interval.
A long ball through by Scott Arfield allowed Steve Lovell to get in behind Ross Tokely and in his attempts to win the ball, he was adjudged to have pulled down the Bairns striker.
Referee Eddie Smith seemed to consult his linesman before bring out the red card, much to the anger of Caley Thistle manager Terry Butcher.
Despite going a man down, Inverness still looked the likelier to open the scoring and almost took the lead three minutes into the second half as Carl Finnigan had just about enough on his misplaced header to clear the bar.
The Bairns did eventually up the tempo and substitute Mark Stewart came close to making a dramatic entrance on 59 minutes as he beat Michael Fraser to a long bouncing ball, but his lob was headed clear by the back-tracking Russell Duncan.
In a bid to find a goal, Bairns manager John Hughes brought on Michael Higdon and within three minutes the sub had made an immediate impact.
Jackie McNamara's low cross was perfect for Higdon, who guided it beyond the helpless Fraser to give the visitors a barely deserved led with 68 minutes gone.
Finnigan then passed up a wonderful chance to secure the win for Falkirk as he missed an open goal from less than six yards on 85 minutes and the Bairns were so nearly made to pay two minutes later, but Brian Kerr's shot from 15 yards flew narrowly over.
Russell Duncan also had a chance moments later, only to direct his shot straight at Mallo having had a clear sight of goal.
It was the last chance for Caley Thistle as their short stay in the SPL was brought to an unwanted conclusion.