Head coach Paul Sheerin made one change to the starting eleven with Ryan Williamson making his first start since recovering from injury, with Gary Miller making way.
The away side had an early chance when Ethan Ross found space out wide and nearly caught out Paddy Martin with a lofted effort. The goalkeeper was beaten but the ball was eventually cleared on the line.
Dario Zanatta was next to fire a shot at goal with a short free kick routine catching out the Bairns defence as the Kirkcaldy side controlled the opening exchanges.
There was no love lost between the sides and Reghan Tumilty was booked on 11 minutes for a needless lunge on Leon McCann.
Falkirk looked to have taken the lead when Callumn Morrison was played in one on one, but his drive from an acute angle crashed off the post. Resolute defending from Paul Dixon kept the score level when Zanatta broke free in front of the goal. The veteran’s last ditch tackle was perfect and won a goal kick as the match ebbed and flowed.
On 20 minutes Raith were reduced to ten men as Tumilty received a deserved second yellow for lashing out at Craig McGuffie.
Raith boss John McGlynn responded immediately with a tactical substitution seeing ex-Falkirk winger Aidan Connolly sacrificed Frankie Musonda, much to the enjoyment of the home support.
Ross Matthews broke the deadlock with a driven effort from outside the box to give the depleted away side the lead, with the Bairns paying the price for giving the midfielder space to sneak his effort into the far corner on 29 minutes.
Charlie Telfer and McGuffie both had efforts from range that failed to trouble Jamie McDonald in the Raith goal as they struggled to make use of the extra man advantage.
The visitors nearly doubled their lead just before the break after Liam Dick freed himself in the box from a free kick and headed narrowly wide.
Falkirk’s talisman Morrison equalised on 52 minutes with a placed effort into the far corner, meeting Williamson’s cross in the box as the Bairns finally found their bearings in front of goal.
The home side took confidence from the goal and thought they had turned the tie on its head moments later when captain Steven Hetherington slotted home after a stramash in the box, but the assistant referee already had flagged for a foul.
On 67 minutes Williamson’s injury hell continued as he went off for Miller after going down without anyone in his vicinity.
Aidan Keena came on for McCann with ten to go as Falkirk went two up top looking for a winner, with Raith’s backline having been relatively comfortable since the equaliser.
The Bairns paid the ultimate price for their lack of attacking threat four minutes from time when the visitors scored on the break. Ross snuck through the despairing Falkirk defence and blasted the ball past Martin to send the travelling support berserk.
John McGlynn’s side had the last laugh, holding out for a superb victory and a place in Monday nights fourth round draw.