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:
Offaly And Longford Chase Semi-Final Spot In Division Four
NFL: Laois Travel To Fermanagh For Crucial Division Three Encounter
Gold Cup Takes Centre Stage On Final Day Of Cheltenham
Offaly TD Demands Stronger Ticket Touting Laws As Six Nations Prices Hit €3k
Offaly Travel To Dublin For Fourth Round Of National Camogie League
Athlone Town Get Title Defence Underway Tomorrow
Shane Lowry Left With Work To Do After Horror 18th At Players Championship
NFL: Must Win Game For Westmeath In Division Three
Westmeath County Council To Host Civic Reception For Athlone Town
Midlands Players Named In Ireland Squad For Showdown With Scotland
Irish Athletics Legend Ronnie Delany Dies Aged 91
Shane Lowry And Rory McIlroy In Action At Players Championship
NFL: Potential Make Or Break Weekend For Midlands Sides
Play Off Spot On The Line For Portlaoise Panthers This Weekend
Athlone Town Host Cobh Ramblers In First Division
Cheltenham Day Two: Il Etait Temp Takes Home Victory In The Champion Chase
Construction Begins On GAA Club Grounds In Laois
Tullamore Squash Club Recognised At National Awards
CCFL: Willow Park Stay Top Of Premier Division
Shane Lowry Back In Action At Player's Championship