Quirke, who scored three second-half points after coming on as a half-time sub against Dublin at Croke Park last month, was superb in atrocious conditions as heavy rain and strong winds ensured that good football was almost impossible.
The teams scored seven points between them in the first half, with Moyle Rovers holding a 0-4 to 0-3 interval lead, before Quirke took over with a fantastic strike just 12 seconds after the restart.
From the throw-in, the impressive Peter Acheson gained possession before embarking on a run straight through the heart of the Arravale defence.
Acheson offloaded to Quirke, who buried a rising drive past Eric Higgins from 10 yards.
That goal handed Moyle Rovers the breathing space they had been craving and as the game descended into a mud-bath, the seven-time county champions had little difficulty maintaining their lead.
Quirke made the game safe in the 51st minute when he produced another top class finish for his second goal, with Acheson again the provider.
Quirke had also struck the upright in the first half as Moyle Rovers threatened and he also judged the wind perfectly to score a free and clip over a point from play.
Moyle Rovers had led by 0-4 to 0-1 before Arravale came back into contention with points from Timmy Dalton (free) and Andy Lacey before half-time.
But Arravale managed just two points in the second half as Moyle Rovers, without injured pair Declan Browne and David McGrath, called upon their vast reserves of experience to close the game out.
Scorers for Moyle Rovers: P Quirke 2-2 (0-1f), P Shanahan 0-3f, P Acheson 0-1.
Scorers for Arravale Rovers: D Lowry 0-2 (1f), A Lacey, T Dalton (f) & B Lowry 0-1 each.
MOYLE ROVERS: I Browne; D Conway, R Power, A Campbell; R Desmond, B Mulvihill, S Keating; M Dunne, N Fitzgerald; S Carey, L Boland, P Shanahan; J Shanahan, P Acheson, P Quirke.
Subs: D Dwyer for Desmond (h.t.), L Cronin for Boland (42), J Lonergan for J Shanahan (52), S Foley for Carey (60), D Lyne for Dunne (60).
ARRAVALE ROVERS: E Higgins; R O’Connor, B Jones, J Hayes; S Leahy, D Leahy, P Ryan; S Spillane, D Kiely; R Kiely, A Lacey, M O’Dwyer; T Dalton, D Lowry, B Lowry.
Subs: S Quinn for Ryan (50), S O’Meara for Lacey (53), B Glasheen for Jones (57), F O’Reilly for B Lowry (58), N Sheehan for D Lowry (60).
Referee: Keith O’Brien.