However, it was level again when a cross struck Sean Mackie's hand and midfielder Matty Todd slotted the Pars' second spot kick.
Falkirk thought they had won it when Liam Henderson bundled home after Oluwayemi failed to gather a late corner, but Dunfermline swept up the other end and opposition centre-half Kyle Benedictus headed in from a corner of their own.
The point leaves the Fife side two points behind Hamilton Academical but 10 ahead of Airdrieonians in what could be John McLaughlan's only game as caretaker as the club appear to be closing in on a successor to James McPake, who was sacked on Monday.
Hamilton host Airdrieonians on Saturday as Livingston have the chance to narrow the gap again at the top as they visit managerless Raith Rovers.