SCORERS: Dunfermline - Geggan (68); Falkirk - Taiwo (55, 60)
Minutes after his introduction, the 18-year-old, who already has two goals to his name this season, danced past a host of challenges inside the box before teeing up Taiwo for the opener.
And his fancy footwork was on show again on the hour mark, neatly slipping the ball into the path of Taiwo, whose flicked finish from just inside the box was wonderful.
Dunfermline, who had wasted unforgivable chances to open the scoring in the first half through Michael Moffat and Jon Page, did find the net through an Andy Geggan header, but could not force an equaliser.
Biabi, who had made such an impressive impact for the Bairns, then soured the evening for the visitors with an act of incomprehensible stupidity, headbutting Ross Millen after a running battle between the pair.
The first incident of note in what would become a fractious affair should have seen Dunfermline claim the lead. A sumptuous free-kick delivery from the left foot of Ross Forbes was perfect for Page but, from all of two yards, he somehow fired his shot against the legs of Jamie MacDonald.
Faissal El Bakhtaoui then produced a stunning delivery onto the head of Moffat, who somehow steered his effort wide from six yards. While not quite as remarkable as Page’s miss, it was still an opportunity which Moffat – scorer of 27 goals for Ayr United last term – would expect to convert with consummate ease.
The decision by Falkirk manager Peter Houston to replace both Blair Alston and Alex Cooper with Biabi and Craig Sibbald after just 50 minutes illustrated his discontent at an underwhelming showing in Fife. It proved to be an initially inspired move. Within minutes of the change, Biabi had wriggled free inside the box before providing a superb cut-back for Taiwo, who rifled a superb low finish past Ryan Scully from 18 yards.
And Taiwo, scorer of two goals in two years at Hibs, matched that tally in the space of five minutes as he latched on to another neat Biabi pass inside the box before flicking the ball nonchalanty into the far corner with the outside of his foot.
Dunfermline would not go quietly into the Fife night, however, and Geggan converted a superb Millen free-kick.
Biabi, who felt Millen had stamped on him while on the ground after 76 minutes, then took centre stage again for rather less positive reasons. His reaction to the claim being waved away was to chase the Pars full-back and headbutt him in front of referee George Salmond.
Inevitably, he was dismissed, and he had to be dragged away – and ultimately chaperoned 60 yards to the tunnel – by teammate Olumide Durojaiye. “He won us the game then nearly lost it,” was manager Houston’s frank assessment of Biabi’s contribution.
But, despite a late onslaught, Falkirk held on to claim their place in the last eight.
Dunfermline: Scully; Millen, Martin, Page (Williamson 65), Drummond; Falkingham, Geggan, Spence, Forbes (Ugwu 65); El Bakhtaoui, Moffat. Subs not used: Goodfellow, Thomson, Graham, Byrne, Smith.
Falkirk: MacDonald; Maybury, Vaulks, McCracken, Dick; Taiwo, Durojaiye; Alston (Sibbald 50), McGrandles (Leahy 84), Cooper (Biabi 50); Loy. Subs not used: Bowman, McGeever, Grant, Shepherd.