Veteran defender Brian Whelahan's 30th-minute goal proved crucial as Offaly edged out a dogged Dublin side 1-17 to 0-17 at Parnell Park.
Whelahan, playing at left half-forward in his first game of the season, was played in by Brian Carroll for the score with the sides level at 0-07 apiece.
Carroll topped up the goal with two more points for a 1-09 to 0-07 break lead for the Faithfuls.
Centre forward David Curtin kept the Dubs in the hunt with his 0-08 tally. Alan McCrabbe, who smashed over four points, was very close to a goal but Ger Oakley blocked his shot away.
Curtin accounted for the majority of Dublin's scores in the first half, and he was central to the hosts pushing Offaly to the finish in front of a 7,122-strong crowd.
With 20 minutes remaining, Offaly were 1-13 to 0-09 clear but a four-point burst from Tommy Naughton's home side - with Curtin, John McCaffrey and Stephen McDonnell on target - saw Faithful nerves jangling.
After McCrabbe's goal chance went a-begging, Curtin pointed the resultant free to make it a three-point game. With ten minutes to go, the Dubs, who struck 12 wides to Offaly's seven, desperately needed a goal, but it just would not come.
In a tit-for-tat finish, Carroll (free), Daniel Hoctor and substitute Eddie Bevans pointed for the visitors, McCrabbe (0-02) and Curtin (free) replied, yet Carroll had the final say with an excellent point from wide out on the right flank.
Dublin: G Maguire; P Brennan, K Ryan, T Brady; D O'Reilly, M Carton, G O'Meara; D Sweeney, J McCaffrey (0-01); L Ryan (0-01), D Curtin (0-08 (5f, 1 '65')), J Kelly; K Flynn (0-01), A McCrabbe (0-04), S McDonnell (0-02).
Subs used: E Moran for Sweeney (45 mins), P Carton for Flynn (65).
Offaly: B Mullins; B Teehan, P Cleary, D Franks; K Brady, R Hanniffy, G Oakley; D Hoctor (0-02), D Tanner (0-01); D Hayden (0-02), G Hanniffy (0-03), B Whelahan (1-02 (2f)); B Carroll (0-06 (4f)), J Bergin, A Egan.
Subs used: A Hanrahan for Egan (45 mins), E Bevans (0-01) for Bergin (55), N Claffey for Brady (57).
Referee: Joe Kelly (Wexford).
