The win seals Offaly a meeting with Wicklow this weekend.
Offaly are into the semi-finals of the Tailteann Cup.
The Faithful secured their place in the final four following their 1-22 to 1-17 win at home to Wexford on Saturday.
Mickey Harte and Declan Kelly's side trailed by six at the break but outscored their opponents by 1-12 to 0-4 in the second half, with Jack Bryant getting his side's all important goal.
Offaly now turn their attention to a clash with Wicklow this Saturday at Croke Park for a place in the decider for the first time.
Harte says they dominated the game:
Mickey Harte and Declan Kelly spoke to Midlands 103 commentator Brian Gavin after the game in Tullamore:
Our coverage of Offaly against Wexford is with thanks to Leahy Midland Auctioneers & BER Assessors, if you're thinking of selling or buying a property or need an energy rating then get in touch with John - visit leahyauctioneers.ie
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