The home side claimed their place in the final with goals from Ger McCarthy and Colm Foley seeing them to victory.
The first half was barely two minutes old when Finn Harps were awarded a penalty after Seamus Kelly had upended Fergal Harkin inside the area. Kelly guessed the right away to deny Alex Nesovic, and after that St Patrick's created several chances, with McCarthy twice coming close.
Then, with seven minutes to go in the first half, Paul Byrne swung in a free from the right and St Patrick's centre half Colm Foley was perfectly placed to head past Graham Downey.
And from another set piece in injury time, McCarthy headed home Robert Griffins corner at the far post.
The second half saw Finn Harps on top but, having pulled a goal back through Kevin McHugh on 63 minutes, were unable to conjure up a second score despite some intense pressure.
ST PATRICK'S ATHLETIC: S Kelly; Croly, Foley, Maguire, Burke; Griffin, Byrne, Osam, R McGuinness; L Kelly, McCarthy. Sub: Harris for McGuinness (75 mins).
FINN HARPS: Downey; Fitzhenry, Dykes, S Bradley; Kenny, Harkin, McGranaghan, Tierney, Minnock; Nesovic, McHugh. Subs: Mohan for Dykes (61 mins), Bonner for Nesovic (82 mins).
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