They now need a point against Derry next week to fend off Leitrim.
Offaly were beaten by Tipperary in their Division 3 Allianz Football League clash yesterday.
It finished 1-16 to 16 points in Semple Stadium.
Conor Sweeney was the thorn in the side of Offaly, scoring the decisive goal and winning a number of key frees in the game.
The result leaves the faithful county in 6th place in the table, ahead of winless Louth and Leitrim, who have a game in hand over Offaly.
John Maughan's charges welcome Derry to O'Connor Park next week knowing a draw would stave off relegation worries for another season.
Maughan says they missed a lot of chances throughout the game:
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