Greg Aitken awarded a penalty is each half, the second a particularly spot call, to help send the Rovers through at a sunny Stark's Park.
The outlook was not bright for the Bairns however who laboured throughoiut the 90 minutes on a heavily watered artificial pitch and even missed a penalty of their own late on through Cahrlie Telfer.
There was little Falkirk chances of note, and to call Gregor Buchanan's side netting effort and a diving header from Denny Johnstone the closest the Bairns came says a lot about how limited the Bairns were when taksed with carving open a tioght-packed and hard-working home defence.
HOW IT HAPPENED: Matchday Live blog - Raith Rovers v FalkirkThe same couldn't be said at the other end and Falkirk were caught napping for the first goal when Iain Davidson's header across goal was not cleared and Michael Miller - a former Bairns trialist - had plenty of time to seize poissession. When he did he was bundled down by Mark Durnan which gave the referee little option.
Regan Hendry took the opportunity and beat Robbie Mutch with a low strike to the goalkeeper's left.
Falkirk toiled. Charlie Telfer was booked for a frustrated tug on the jersey of the goalscorer after becoming mired in a midfield battle which isn't a particular forte of his many ball-playing talents.
PLAYER PROFILE: Gary MillerLouis Longridge's cross was headed wide by Johnstone in the most threatening move the Bairns could muster though the captain Buchanan did send a tame acrobatic effort into the side netting from a corner that Rovers couldn't clear.
The uninspiring fare continued in the second period and Falkirk's task doubled when Ian mcShane was adjudged to have pushed Dylan Tait over with the ball running out of play. It bwas a soft call, and probably needless too with the Bairns threatening so little at the other end, but Hendry made sure with a powerful spot-kick high beyond the Bairns goalkeeper Mutch, who was literally the team's last line of defence with no other goalkeeping option named on the bench.
It sapped what little hope the visitors had and the McDermid away stand was too deflated to join in an offer to 'stand up if you hate the Pars' chant at the home end.
Ray McKinnon made three attacking changes with Declan McManus and Aidan Connolly on for Lewis Moore and Robbie Leitch, then Connor Sammon replacing Denny Johnstone with 20 minutes to go. Johnstone had been the Bairns' best attacking outlet and could have done better with a header shortly after the Bairns' second concession but couldn't get enough on his header.
The introduction of Lewis Vaughan after a nine-month injury lay-off boosted the home side more and the sub hit the crossbar with a stunning free-kick with 15 still to play.
He was i nvovled again as the woodwork was struck again with nine minutes to go, but for the wrong reasons. Vaughan fouled Charlie Telfer in the box and Greg Aitken awarded his third penalty of the afternoon. Telfer took it himself and smashed a powerful effort off the bar to sum up Falkirk's afternoon and exit from the competition.