Having been fortunate to lead at the interval through a Harry Murphy penalty, Fulham then failed to score for 26 second-half minutes and when Parnells forward David O’Sullivan converted his sixth free of the day, a replay looked on the cards.
However, the inspirational Lorcan Mulvey then led a late Fulham rally, scoring off a swift counter-attack, before three injury-time points sealed victory.
Scorers for Fulham Irish: H Murphy 1-2 (1-0pen, 1f), L Mulvey, F McVey 0-2 each, J Boyce, J Ryan (f) 0-1 each.
Scorers for Parnells: D O’Sullivan 0-6 (6f), F Niblock 0-1.
FULHAM IRISH: D Traynor; G O’Hare, C McClean, M Conway; A Savage, S Mulligan, J Boyce; L Mulvey, P Walsh; S Molumby, H Murphy, I Barrett; J Ryan, S Maguire, D Connolly.
Subs: F McVey for Molumby (21), N Nicholson for Connolly (43), J Reilly for Maguire (50), G Murphy for O’Hare (52), P McKernan for Walsh (56).
PARNELLS: E Byrne; K Culhane, B Kerr, T Quaid; J Niblock, S Bradshaw, N Tuohy; D Donnelly, N Corkery; D McCarthy, D Shallow, D O’Sullivan; E Flaherty, F Niblock, A Mulholland.
Subs: E O’Connor for Donnelly (42), R Dempsey for F Niblock (53), A Murray for McCarthy (53).
Referee: M Maher.