Not since 1990 has a “non-league” side – St. Francis – reached the last four of the competition.
But two first-half goals paved the way to victory for the Donegal side who are through to the semi-finals for the first time since 1999.
And when Avondale had goalkeeper Danny O’Leary sent off mid-way through the second-half it was curtains for the Munster Senior League outfit.
The Cork side began positively and Ray Lally went close with a header that forced Harps’ goalkeeper Conor Winn to tip the ball around the post.
But Harps took the lead on 11 minutes with Gareth Harkin sliding in to connect with a Brian McGrory cross to steer the ball past Danny O’Leary.
While the visitors mustered up the occasional counter-attack Harps began to control the game.
And their efforts were rewarded on 37 minutes as veteran Kevin McHugh raced into the box before passing for the unmarked Damien McNulty who rushed in to fire past O’Leary.
Harps could have added a third before the break with substitute Pat McCann having a shot blocked while David Spratt was on hand to make a goal-line clearance.
McHugh forced in a third from close range on 57 minutes and five minutes later Avondale had goalkeeper O’Leary sent off for impeding Harkin.
McHugh duly obliged from the penalty spot.
Roy Long bagged a consolation goal for Avondale six minutes from time.
Its 40 years since Finn Harps won the FAI Cup for the one and only time in the club’s history.
The dream is now once again alive in a year that sees the club celebrating its 60th anniversary.
Harps’ promotion hopes were effectively ended last month, but the sleeping giants of the north-west have suddenly seen their season rejuvenated.
FINN HARPS: Winn; McNulty, P. Mailey, Cowan; McMonagle, Coll; Funston (O’Callaghan 66), J. Mailey, Harkin; McHugh (Tiofack 75), McGrory (McCann 37).
AVONDALE UTD: O’Leary; Horgan, Mulconry, Spratt (Kiely 61), Lally; Kelly, Warren (Connolly 61), Murphy, McCarthy; R. Long, D. Long (O’Keeffe 62)
Referee: R Matthews (Dublin).