The failure of their forwards to convert their chances resulted in Donegal making the long journey home from Tullamore in disappointed mood following their defeat by defending league champions Offaly.
The holders were in a happier frame of mind after recording their first win in five outings, but they left it very late to secure the points as the decisive goal was scored by Vinnie Claffey in the 60th minute.
In a game that produced mixed fare for an attendance of 3,500, Offaly just about deserved to finish on top, although both sides had cause to rue faulty finishing. This was particularly true of Offaly in the first half, with their usually reliable place-kicker David Connolly missing a number of easy frees.
During that opening free-ridden half Donegal looked the sharper side, but scores were level three times before the visitors forged a 0-6 to 0-4 interval lead thanks to three late points from frees by Tony Boyle (two) and John Duffy.
Interval changes by Offaly saw Pascal Kelleghan and Donie Ryan replace Ronan Mooney and Colm Quinn, with Sean Grennan moving out to partner Ciaran McManus at midfield. The result was an improved performance, and although another Duffy free stretched Donegal's lead on the resumption, the holders gradually began to assume control.
Unanswered Offaly points by McManus from a 45, impressive newcomer Barnie O'Brien and Donie Ryan brought the holders level with 11 minutes remaining. A draw looked the likely outcome until Claffey's decisive strike right on the hour when he applied the close-range finish to a splendid movement. Donegal tried hard to save the game but Boyle's injury-time point was their only reward.
OFFALY: P Kelly; C Daly, J Ryan, D Foley; J Kenny, F Cullen, T Coffey; P Mulvihill, C McManus (0-2); C Quinn, B O'Brien (0-1), V Claffey (1-1); P Brady, S Grennan, D Connolly (0-2). Subs: R Mooney for Mulvihill, P Kelleghan for Mooney, D Ryan (0-1) for Q.uinn
DONEGAL: P Callaghan; D Diver, J J Doherty, N McGinley; R Sweeney, O Reid, N McCready; J McGuinness, J Ruane; J Duffy (0-3), A Sweeney, B Ward; B Roper (0-1), T Boyle (0-4), B Devenney. Subs: B McLaughlin for Ward, N Hegarty for A Sweeney, B Gillespie for Devenney.
Referee: S Prior (Leitrim).