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And the semi-final replay went the way of Alan Matthews' Town side as they initially took the lead through winger John Martin on 32 minutes.
A flicked header from former Bray Wanderers' striker Paul Keegan played Shane Barrett in down the left wing and his low cross was driven home at the back post by Martin for an ideal start.
It stayed 1-0 until after the break, and although Longford's Dessie Baker struck the Drogs' crossbar a minute after the restart, United soon equalised as Declan O'Brien grabbed his sixteenth goal of the season.
On 49 minutes, Barry Molloy slipped the ball through for the impressive O'Brien to lob his namesake Stephen O'Brien in the Longford goal.
Neither side could make the breakthrough in normal time and it was left to Dillon in the first period of extra time to split the sides.
He booked Longford's place in their second Cup final of the year - following on from their 2-1 eircom League Cup final triumph over Bohemians in August - as he curled home from 25 yards after 114 minutes.
Matthews' charges travel to Cork for a Monday night league clash next, whilst Paul Doolin's Drogheda face into a tough Friday night top-of-the-table clash with Premier Division champions Shelbourne (live RTE 2, 7.30pm).
The second-placed Drogs have lost their last two league games to Cup finalists Waterford and Longford.
Drogheda United: Rogers, Flanagan, Sandvliet, O’Connor, Grey, Lester, Molloy, McClare (Freeman 110 mins), Cronin, O’Brien, Myler (Rooney 79).
Longford Town: O’Brien, Dillon, Prunty (Perth 98), Gartland, Ferguson, Murphy, Fitzgerald, Martin (Lavine 87), Barrett, Keegan, Baker.
Referee: A Kelly (Cork)