Second half goals from Declan McManus and Conor Sammon gave the Bairns a replay victory on a chilly and wet evening at Westfield.
It was enough to earn a slot on primetime Saturday night TV on february 8 in the televised fifth round clash.
This was a meeting of last season's 22nd and 23rd placed clubs in the Scottish football league structure and it showed with little to separate the sides in the first half, just as had been the case at Gayfield earlier this month.
HOW IT HAPPENED: Matchday blogFalkirk had the better chances of the first half but Arbroath had the balance of play.
Aidan Connolly fired a half-volley just wide in an effort reminiscent of his two goals on Saturday against Forfar and Morgaro Gomis had another shot on the bounce deflected over on the stroke of half-time.
But Arbroath had the measure of the Bairns and restricted the home side to attacks on the break, often snuffing them out long before they troubled Derek Gaston.
Falkirk too though held fairly firm at the back and Robbie Mutch dealt with much that was asked of him, particularly in the early stages where only some last-gasp defending kept Arbroath at bay with blocks and deflections wide.
The Bairns should have had the lead when McManus and Sammon both barrelled through on 41 minutes with the Irishman having the final finish but firing straight at Derek Gaston when one-on-one after Euan Anderson had overruled his linesman for an offside call, much to the anger of the visitors' defence.
The second half was barely two minutes old when McManus gave the Bairns the lead, spinning in the six-yard box to fire his side ahead after Gregor Buchanan's header had struck Mark Durnan and left Gaston prone on the ground.
It proved a calming influence on the Bairns and Falkirk assumed control of proceedings though did almost concede to a swift break by Luke Donnelly. However the 'old legs' of Paul Dixon, described in a pre-match Arbroath scpouting report circulated online, raced back to deny the striker and maintain Robbie Mutch's clean sheet record.
It remained intact for the duration and Lee Miller and David mcCracken's enviable unbeaten record as managers was asured too when McManus burst into the box in the 66th minute and cut-back for his strike partner to prod over the line.
That proved Sammon's final act and he was replaced by David McMillan as the management cycled their squad with a tough run of fixtures to come.
The changes faield to interrupt Falkirk's composure and the Bairns eased into the fifth round comfortably at the expense of Dick Campbell's side.