Falkirk defender McCracken thundered home a low shot from the edge of the penalty area for only his third goal for the club when it seemed the Bairns would have to settle for a draw.
Hibs striker Paul Heffernan had earlier seen a shot blocked and Falkirk midfielder Rory Loy fired into the side-netting soon after to set the trend in a see-saw match.
Heffernan headed just off target before the half-hour mark and Falkirk duo Will Vaulks and Peter Grant both went close.
Hibernian midfielder Sam Stanton then saw a long-range effort fly inches wide at the end of a scoreless opening period.
Vaulks had one effort blocked by Hibs goalkeeper Mark Oxley early in the second period and pulled another effort wide, while Loy lifted his shot over the crossbar shortly afterwards.
An appeal for a penalty from the away side was waved away by referee Stephen Finnie when Scott Allan went down in the area before the visitors were undone by McCracken’s late piledriver.