Ross County 0 Falkirk 1
County had enough chances to win the game, but it was former Airdrie United striker Alan Gow who grabbed the winner after an hour's play with a superbly taken strike.
Falkirk made a lively start and a Gow cut back was whipped into the box by Liam Craig but Jim Lauchlan rose high in the box to head clear.
At the other end Sean Higgins set up John Rankin with a good chance but County's top scorer was twice denied by Bairns keeper Allan Ferguson before he fired into the side netting.
Steve Thomson fed Pedro Moutinho in the 12th minute with a defence splitting pass but the Portuguese striker's first touch let him down and the ball rolled through to County keeper Stuart Garden.
This replay was played in typical cup tie fashion and the home side were giving their Premier League visitors a few scares early on.
Don Cowie curled a left-foot shot wide of Ferguson's right-hand post, then Mark McCulloch's header was cleared off the goalline by Craig.
Alex Burke had the best chance of opening the scoring when Kevin McKinlay teed the ball up for him, but his shot was well saved by Ferguson.
Play raged from end to end, and Moutinho was in the action again when he blasted a shot high over the crossbar from the edge of the six yard box.
Andy Lawrie replaced Jack Ross on the right-hand side of the Falkirk defence in the 26th minute.
Falkirk won a free-kick three minutes from the break. Gow's initial shot was blocked by the County wall and Thomson fired the rebound wide of Garden's right-hand post.
Both sides made changes for the start of the second half. David Winters took over from the injured Burke up front for County and Jean Lescinel made way for Mark Twaddle.
County were awarded a free-kick in the 49th minute but Rankin's left-foot effort dipped over the crossbar.
Then Cowie swept another free-kick on to the six-yard line and Winters headed over as County came close to the opener.
The home side were applying most of the pressure but it was Falkirk who broke the deadlock in the 62nd minute.
Craig released Gow on the left and the midfielder turned inside and left fly with a vicious left-foot shot that ended up in the far corner of the net.
That seemed to knock the stuffing out of County and Falkirk looked well in command in the final stages, although the home side came close with free-kicks from Higgins and Rankin.