A goal from a suspiciously offside position by Carl Finnigan gave Falkirk the half-time lead and Mark Stewart sealed the victory with a slick second-half finish before Scott Arfield and Finnigan added the gloss late on.
Terry Butcher will point to his side's poor finishing as the difference between the teams and Dougie Imrie and Adam Rooney were both guilty of glaring misses that turned the match.
There is now just one point between the sides at the bottom with Inverness enjoying the slimmest of advantages. But this battle to avoid the drop threatens to go right to the wire.
With the spectre of relegation hanging over both sides it was an understandably cagey opening with the midfield a very congested area.
Patrick Cregg's throughball sent Finnigan chasing through but Ryan Esson had plenty of time to come off his line to claim the ball.
The first effort at goal came from the home side after 17 minutes when Mark Stewart collected Jackie McNamara's throw-in and found a yard of space to fire a half-volley over the bar.
But it was Inverness who missed a great chance midway through the half when Steven Pressley got caught under a high ball and Adam Rooney took the ball round Dani Mallo only to then screw his shot wide from a tight angle with the empty goal at his mercy.
The game desperately needed a goal and it came after 37 minutes albeit from a suspiciously offside position.
Michael Higdon threaded the ball along the 18-yard line and Jackie McNamara slipped a first-time pass into the six-yard box where Finnigan looked isolated as he slipped the ball home.
Finnigan turned to the linesman to check he was onside and the flag stayed down to the delight of the home fans.
Inverness almost hit back immediately through Imrie's dipping 25-yard free-kick that was fisted away by Mallo low to his left.
Grant Munro failed to clear Tam Scobbie's free-kick giving Finnigan another chance but his effort was scuffed and Esson saved easily.
Falkirk had an early chance in the second half to wrap up the points with a swift break out of defence. Scott Arfield had options on either side through Stewart and Finnigan but he under-hit his pass to give Inverness a major let-off.
But the Bairns were edgy and some slack defending let Richie Foran have a shot at goal on the turn. Mallo flapped at the ball which spilled out to Rooney who fired wide under pressure from Scobbie.
And the visitors missed another great chance when Rooney ghosted past Pressley and found Imrie with a low cross. However, the little winger managed to fire wide from only three yards out.
How vital that miss proved as Falkirk wrapped up the points with a route one goal. Mallo's long clearance was nodded on by Higdon and Stewart showed Munro a clean pair of heels before slipping a low finish past Esson.
It wasn't pretty but Stewart deserves credit for a cool finish in such tense circumstances.
Imrie missed the target again from 12 yards before Inverness were reduced to ten men in the closing stages.
Finnigan nipped in front of Esson and looked certain to score when the keeper took his legs away.
Esson was shown a straight red card and a penalty was awarded. Michael Fraser came on as a substitute keeper and his first job was to pick Scott Arfield's penalty out of the back of the net.
And with Inverness now run ragged, Finnigan tapped home the fourth in stoppage time from Neil McCann's cross.