A lively encounter was eventually decided by a crisp Peter Durrad finish in the 112th minute.
Salthill Devon, bottom of the First Division table, gave the Saints a tough game, but the favourites were inspired by Jake Kelly, who scored two and then crafted the winner.
Anto Flood had a goal disallowed for Pat's in the 31st minute after he was deemed to have handled in the build-up and moments later he headed over.
Seven minutes after the restart Salthill stunned the visitors when Derek O'Brien's cross was met by a firm Enda Curran finish. The Saints responded when a controversial Jake Kelly free kick was deflected into the Salthill net.
In extra-time Brian Geraghty nudged Salthill ahead in the 101st minute, but Pat's came swinging back. Kelly replied on 105 minutes for Pat's and then his centre ensured Durrad landed the decisive blow.
Salthill Devon – Keane; Gaul, Fadden, Geraghty, McGlynn; Biansumba (Horgan, 67), Enubele (Kelly, 117), Harding, O'Brien; Tomanica; Curran (Collins, 103).
St Patrick's Athletic – Ryan; Maher, Gannon, Price, Carroll; Murphy (Durrad, 81), McFaul, Boyne (O'Brien, 67), Keegan (Chindea, 106); Kelly; Flood.
Ref – P Sutton (Clare)