Killian Brennan gave St Pats the lead in the 20th minute from a well executed free kick.
Just before the half hour Packie Mailey levelled the game with a strong header at the far post.
By the break Harps were 3-1 down after Sean Hoare and Conan Byrne scored in the final ten minutes of the half.
Pats went on to score three further goals from Brennan, Byrne and Christy Fagan to seal their place in the final.
Gareth Harkin was shown a red card for a two footed challenge and Harps boss Ollie Horgan was also sent to the stand for arguing with officials about Harkin’s dismissal.
Harps end their season next Sunday when they entertain First Division champions Longford Town at Finn Park.