The Glenties outfit led 0-3 to 0-1 and 1-3 to 0-3 after Dara Gallagher's goal.
But Glenties levelled within two minutes as Molloy notched his fifth point of the contest.
Frees from Molloy and Gallagher put Glenties ahead again and Coalisland missed several late chances to level.
After McNeice reduced Glenties' lead to the minimum, the advantage was suddenly four points when Gallagher blasted emphatically to the net on 18 minutes.
Dermot Molloy's three points helped Glenties lead 1-7 to 0-6 at half-time but Coalisland hit 1-3 without reply to lead with Plunkett Kane netting.
Keeper Curran's two points kept Coalisland in touch on the scoreboard but Glenties still had a healthy 1-7 to 0-6 advantage by the break.
Anthony Thompson knocked over a couple of frees for Glenties, for whom young Darragh Gallagher scored an excellent point at the start of the second period.
BBC: SPORT | Northern Ireland | Gaelic Games | Mayobridge 0-10 1-05 Glenties
Clarke had put Cross ahead in the fifth minute but Glenties hit three of the next four scores to take a merited 0-3 to 0-2 advantage.
Glenties, who had a wind advantage in the first half, went ahead in the second half thanks to a Leon Thompson goal, which saw them lead 1-4 to 0-5.
BBC: SPORT | Northern Ireland | Gaelic Games | Mayobridge 0-10 1-05 Glenties
Another Dara Gallagher point restored Glenties' lead before half-time but despite their dominance, it was only a one-point game and there was that suspicion that, on the scoreboard at least, Naomh Conaill had not fully exploited their superiority.
Keeper Curran ran up the field on two occasions in the dying seconds to attempt long pot-shots from 45 metres but he failed to find the target both times as Glenties set up their provincial decider appearance against Crossmaglen.
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