John Stewart blasted home a first-half penalty following Michael Higdon's opener and Raith's spirited comeback was ultimately undone by Allan Walker's sending-off at the hands of Craig Thomson.
Mark Campbell deservedly pulled one back but Mark Stewart killed off the second-round contest late on to earn Falkirk their first victory of the season.
Higdon had accused Brines of "bottling" major decisions in his side's 3-0 defeat at Celtic on Saturday while manager John Hughes hit out after he was wrongly summoned by Brines during his half-time team talk.
But the decisions went Falkirk's way on Tuesday night. Raith were enjoying the territorial advantage when Higdon finished off the first chance of the match in the 16th minute.
Mark Stewart returned his pass from the left flank and the big striker slotted home from 10 yards.
The home side lost Robert Sloan to injury midway through the half, with Mark Ferry coming on, but they continued to push forward and built some decent moves.
However, despite some pressure from set pieces, they could not carve out an opening and they were undone by some hesitant defending that led to the penalty.
Raith had harried their opponents well as Falkirk kept possession, to push the ball back into the visitors' half.
But their defence was caught ball-watching after Higdon headed on Lee Bullen's long ball. Mark Stewart cut across the box to reach the loose ball just before David McGurn.
Stewart was already falling over when McGurn crashed into him, but the Rovers keeper made no complaint when Thomson pointed to the spot and booked him.
John Stewart sent McGurn the wrong way as his 35th-minute penalty slammed into the top corner.
The goal took the sting out of the Irn-Bru Second Division side and Higdon had two more half-chances before the break.
The former Crewe striker headed just wide of the far post following John Stewart's cross and then shot a yard over from long range following a good passing move.
Raith recaptured their belief in the early stages of the second half and pushed back Falkirk, who lost Jackie McNamara at half-time.
Gareth Wardlaw almost had a sight of goal as he attacked Andrew Cook's left-wing cross but the ball bounced awkwardly just in front of him and span away.
Raith suffered another blow in the 58th minute when Walker received a straight red card after raising his studs in a challenge on Thomas Scobbie, who had come on for McNamara.
But they kept pushing forward and Wardlaw might have been better shooting after chesting down a long ball in the box; instead his pass for Kevin Smith was cut out.
The home fans' sense of injustice was fired further when Patrick Cregg avoided a second booking following a sliding foul.
But their team's effort was rewarded in the 74th minute when Campbell finished off a slick move from 12 yards.
Smith, out on the left flank, played the ball in front of Ferry's run and Campbell placed his cutback into the bottom corner.
Falkirk finally began to make their extra man count and McGurn blocked brilliantly from Mark Stewart after the ball fell kindly for the Falkirk youngster on the edge of the box.
But the same player was soon celebrating when he headed home a brilliant inswinging cross from Gerard Aafjes to finish the tie off with six minutes left.