The former Celtic boss had warned his side to expect a fast start from Falkirk, but it was Dunfermline who were on top early on, their high press and aggression unsettling the top-tier side.
Callumn Morrison - whose goal helped Falkirk to League 1 title two seasons ago - was through on goal within two minutes but skewed his shot wide from 15 yards.
Falkirk, though, started to show their superior pedigree and defender Filip Lissah perhaps should have done better than head over from 10 yards.
On-form striker Barney Stewart also headed straight at the goalkeeper for what turned out to be the only effort on target in the opening 90 minutes.
It took until the 72nd minute for either side to seriously threaten the stalemate, with on-loan Aston Villa midfielder Ben Broggio firing wide of Dunfermline's far post from 16 yards.
So to extra-time, when Falkirk substitute Kyrell Wilson dragged a snapshot wide before Dunfermline striker Lucas Fyfe twice had the chance to snatch victory.
However, the 17-year-old substitute fired straight at goalkeeper Scott Bain then found the underside of the crossbar from close range.
Ethan Ross was denied by a fine fingertip save from Oxborough and Falkirk substitute Henry Cartwright was shown a second yellow card for simulation.
That turned out to be the final action before the game was settled in the most dramatic style from the penalty spot.