The Tyrone champions were clinging to a one-point lead in injury-time when Charlestown’s Colm Maye saw his attempt for an equaliser from a 13m free strike the hand of a Cookstown player.
The final whistle sounded moments later to signal victory for Fr Rocks but a number of Charlestown players approached referee Gary McCormack to protest that the free should have been retaken as the Cookstown defender had been too close to the ball.
However, their representations were in vain as Cookstown celebrated a famous win that earns them a place in their second IFC decider in four years.
The Ulster representatives had to win this game the hard way, after the Mayo champions had built up a 1-5 to 0-3 lead by half time in normal time, with full-forward Anthony Mulligan scoring the goal on 12 minutes.
Driven on by the outstanding Martin Murray, Cookstown dominated the second half and a fortuitous goal from Murray in the 51st minute levelled the match.
Richard Haran (free) and Conor Mullan then traded scores to force extra-time.
Fr Rocks held the Connacht side scoreless during the extra 20-minute period, while James McGahan’s early point turned out to be the decisive score.
Scorers for Charlestown: R Haran 0-4 (3f), A Mulligan 1-0, C Maye (45) 0-2, M Caffrey 0-1 .
Scorers for Fr Rocks: M Murray 1-1 (1f), C Mullan, S McGarrity, O Mulligan (1f) 0-2 each, J McGahan 0-1.
CHARLESTOWN: D Sloyan; G McLoughlin, D McMeel, S Lenehan; A Higgins, G O’Donnell, D Higgins; T Parsons, E Casey; R Haran, M Caffrey, P Ward; J Owens, A Mulligan, C Maye.
Subs: D Tiernan for Ward; S Morris for Owens; Conway for Maye; K Deignan for A Higgins; B Parsons for D Higgins; J Owens for Conway; C Maye for T Parsons.
Fr ROCKS: M Rea; P McGurk, S Monaghan, D Hughes; R Pickering, M Murray, M Hughes; C Mullan, C O’Hare; S McGarrity, B Hughes, B Mulligan; J Gilmore, O Mulligan, J Quinn.
Subs: B Kelly for D Hughes; J McGahan for B Mulligan; P Kelly for M Hughes; M O’Connor for Gilmore.
Referee: G McCormack (Dublin).