He headed in a cross from Adam Hammill just as the match looked like it was heading for a replay.
McGuire had the best chance of a tame first half when Hammill picked him out with a free-kick but he failed to make proper contact with his header.
Hearts hit back and new signing Laryea Kingston tried his luck from long range but the ball was always drifting over.
Dorus de Vries pulled off two excellent saves at the start of the second half to deny firstly Saulius Mikoliunas and then Michal Pospisil.
Roman Bednar came close late on when his chip hit the top of the crossbar, but it was Dunfermline who were to get the goal.