Galway rescued a draw from the jaws of defeat at Tullamore thanks to Ger Farragher's tenth point of an eventful afternoon.
The Tribesmen looked to be coasting as they took a 0-11 to 1-03 lead into the second half, with Brian Carroll bursting through for Offaly's 13th-minute goal.
However, two goals inside a minute from David Franks and substitute Ger Healion topped off a fantastic second-half comeback from the Faithfuls.
A Franks point edged Offaly ahead again but Farragher provided a last-gasp equaliser.
This keenly-contested encounter at O'Connor Park began with Offaly bursting out of the blocks to lead by 1-02 to 0-02 after 13 minutes' play.
Galway perhaps tried too hard during that period to get up to speed as they hit five wides.
Francis Kerrigan popped over Offaly's opening point after only 15 seconds and after a successful second-minute line ball from Farragher, Ger Oakley and David Forde exchanged points.
Carroll's goal followed as the corner forward got in on the end of a long free from goalkeeper Shane O'Connor and slammed home to the net.
Incredibly, Offaly failed to score again until Carroll flung over a 33rd-minute point. Their early onslaught was quickly brought to an end as Galway accumulated point after point, with four of them from Farragher, during a 15-minute spell.
Ger Loughnane's side dominated possession during the second quarter with Adrian Cullinane, Aoghus Callinan, Kerril Wade and Alan Kerins getting on the scoresheet.
Although a clear five points separated the sides at half-time, Galway should have been a lot further in front, especially having hit 11 wides.
Offaly failed to give up and Joe Dooley's charges came out an inspired force for the second half. They cut the deficit to two points within 13 minutes of the restart.
Although Farragher claimed the first point of the half, the home side were a superior outfit over the third quarter.
The Faithfuls, roared on by the bulk of the 3,500-strong crowd, held a lot of possession in attack, with James Rigney, man-of-the-match Franks, goal scorer Carroll and substitute Daniel Currams suddenly thriving.
Points from Farragher and Kevin Hynes edged Galway into a 0-15 to 1-08 lead midway through the half, but the two goals from Franks and Healion fired a game Offaly side into a two-point lead.
Wing back David Kenny was instrumental in the moves that led to the two goals as Galway were made to pay dearly for lapses in defence.
The visitors pressed hard for scores and two Farragher points brought the sides level with three minutes of normal time remaining.
However, Franks nabbed a late point and although Wade and Farragher put shots the wrong side of the posts, the latter still had time to point the levelling free in injury-time, after a foul on Kerins.
Offaly: S O'Connor; K Grogan, K Brady, C Hernon; D Horan, J Bergin, D Kenny; B Leonard, J Rigney (0-01); D Franks (1-03), G Oakley (0-01), C Mahon; B Carroll (1-03, 0-02f), D Molloy, F Kerrigan (0-01).
Subs used: G Healion (1-00) for Kerrigan (half-time), D Currams (0-01) for Oakley (40), S Dooley for Mahon (68).
Galway: J Skehill; D Joyce, T Og Regan, C Dervan; A Keary, J Lee, G Mahon; A Cullinane (0-01), K Hynes (0-01); A Kerins (0-01), D Forde (0-02), A Callanan (0-01); G Farragher (0-10, 0-05f, 1 '65', 1 sl), I Tannian, K Wade (0-02).
Subs used: F Healy for Callanan (half-time), F Coone for Tannion (53 mins).
Referee: Dickie Murphy (Wexford)
