A nightmare display from home keeper Allan Ferguson plus some clinical finishing from the visitors turned an evenly-matched cup tie into a smooth passage to the semi-finals for Hibs.
The Edinburgh club struck four times in the final quarter of the contest to enjoy a flattering margin of victory. Falkirk were always playing catch-up from the moment Ferguson somehow allowed Derek Riordan's soft free-kick to squirm through his hands for the opening goal after just nine minutes.
The Bairns had actually made the better start and continued to compete strongly after Ferguson's costly blunder. Defender Jack Ross and midfielder Patrick Cregg both shot fractionally over from distance, and there was also a half-hearted penalty appeal when Hibs full-back Steven Whittaker appeared to handle the ball.
Falkirk's best chance came shortly before half-time when a looping header from Kenny Milne was nodded off the goal-line by defender David Murphy.
Hibs were repeatedly stretched by Falkirk's long-ball game in the swirling wind, but the visitors are experts on the counter attack and after Ivan Sproule had missed a glaring chance from 18 yards, Ferguson spilled another Riordan effort and Garry O'Connor rammed home the rebound.
Daniel McBreen's crisp left-foot finish briefly raised Falkirk's hopes again before late strikes from Sproule, scrambled in from point-blank range, Gary Caldwell with a header at the back post, and substitute Steven Fletcher with the aid of a deflection kept Hibs on course for their first cup triumph since 1902.