Fife striker Steven Nicholas netted the decisive penalty after the teams finished all square after 120 minutes.
Former Pars player Craig Lumsden was desperate to face his old side in the next round and opened the scoring after 21 minutes.
Greig McDonald had a shot blocked and Lumsden pounced to hammer in the rebound.
The Highland League side battled back and Kris Brash had to nod Russell Guild's header off the line on 33 minutes.
But the Fifers couldn't clear and when the ball came in Jerry O'Driscoll rose to loop a header over Scott Morrison.
Huntly stunned the Fifers after 43 minutes when they grabbed a shock lead.
Guild did the spadework and gave the ball to Marco De Barros who curved a great effort into the top corner.
McDonald should have leveled after 59 minutes but missed an open goal after Stevie Nicholas set him up.
Gary McGowan was then denied a glorious goal after 60 minutes when he cut inside Brash and side-stepped the keeper but Lumsden headed a shot off the line.
McDonald made amends after 71 minutes when he slammed in an equaliser after Richard Bowman somehow saved Lumsden's header.
Huntly could have won the tie in regular time and probably thought they had done so after 107 minutes when Guild pounced on a Morrison error.
Luckily for the Fifers, McDonald popped up with another leveler two minutes from time to take the tie to spot kicks.
Both sides missed a penalty as the nerves jangled and it was left to Nicholas to win it with the last kick.