The Station Park side came from behind three times to secure extra time, then Rab Douglas made two saves in the shootout to allow Craig Smith to win the tie.
It was harsh on Brechin, who led after six minutes when Andy Jackson got on the end of a Steven Robb pass to score, but Forfar were level within quarter of an hour when Chris Templeman rose to power in Martyn Fotheringham's corner.
Brechin restored their advantage five minutes into the second half, when Neil McCabe fouled Darren Petrie and Alan Trouten converted the kick. Forfar kept coming, though, and with six minutes left, Gavin Mallin beat Graeme Smith.
Four minutes into extra time Brechin were back in front through Allan Walker but another Templeton header hauled Forfar level again before the shootout.