Jim Gavin’s side looked shaky for spells in the first half and trailed by three with 20 minutes to go to a strong-looking Offaly side.
But seven points in a row from the hosts including two from top scorer Dean Rock, who tallied 0-9 in total, put the experimental Dubs at their ease late on.
The result follows their Round 1 win over Maynooth University and means another win over Laois in Portarlington on Sunday will guarantee their semi-final place having missed out last year.
It wasn’t vintage Dublin in wet and windy conditions though Michael Fitzsimons was the only starter from their All-Ireland semi-final defeat to Donegal last August.
Visitors Offaly were fresh from Sunday’s nine-point win over midlands neighbours Laois.
They opened the scoring through Nigel Dunne and asked the more probing questions for nearly 50 minutes. Dunne finished the first half with three points and all but one of Offaly’s forward six made the score sheet.
Dublin continued with rookies Eoin Culligan and John Small in the central defensive positions.
Small was impressive in patches and burst out of defence at one stage in the first-half to roars of approval from the home crowd. But his man, Offaly centre-forward Eoin Carroll also picked off two fine points.
Visiting full-forward John Kavanagh kicked the score of the half after a fine solo run up the right wing. There was a second eye-catching effort from Dunne to close out the half and leave Offaly 0-10 to 0-7 up.
New Offaly manager Pat Flanagan is keen to hit the ground running in 2015 but they were without their county title-winning Rhode contingent.
Still they looked slick and sharp for long spells ahead of their bid for an immediate return to Division 3 football in the spring.
As for Dublin, Gavin was as good as his word and continued to hand lots of game time to fringe players and panellists.
Ballymun’s Sean Currie got a rare start in goals while Graham Hannigan began at left half-back.
There was a midfield pairing of Craig Dunleavy from St Oliver Plunkett’s Eoghan Ruadh and former underage star Emmett O Conghaile.
Up front, Philly Ryan looked lively when on the ball and hit an important point in the second half to finally put Dublin ahead at 0-13 to 0-12.
Rock did the bulk of Dublin’s scoring with five of their seven first-half points and of his 0-9 overall, six were from placed balls. He took his tally to a half dozen as Dublin narrowed the gap to two after the restart.
And while Offaly would reopen a three-point lead with points from Dunne and Bernard Allen, it was as good as things would get for them.
Tomas Brady began the blitz and scored two of their seven points which arrived between the 52nd and 66th minutes.
From a position of difficulty, Dublin were now lording it around the middle and forward third and capitalised on the strong wind at their backs.
Offaly sub William Mulhall pulled one score back but, fittingly, Dublin had the final say as Rock booted his ninth of the evening in injury-time.
Dublin scorers: D Rock 0-9 (six frees), P Ryan and T Brady (0-2 each), E O’Gara, N Scully, E O Conghaile and M Deegan (0-1 each).
Offaly scorers: N Dunne (0-4, one 45, two frees), B Allen (0-3, two frees), E Carroll (0-2), D Hogan, K Mullally, J Kavanagh and W Mulhall (0-1 each).
DUBLIN: S Currie; M Fitzsimons, E Culligan, D Daly; N Devereux, J Small, G Hannigan; C Dunleavy, E O Conghaile; T Brady, D Rock, N Scully; P Ryan, E O’Gara, N Collins.
Subs.: P O’Higgins for Dunleavy (h/t), M Deegan (0-1) for O’Gara (44), S Lowndes for Scully (49), C McGuire for Collins 51, R McGowan for Daly (57), I Kavanagh for Devereux (64).
OFFALY: A Mulhall; E Rigney, P McConway, J Ledwith; B Crombie, C Donohue, D Hogan; G Guilfoyle, R Allen; K Mullally, E Carroll, N Bracken; B Allen, J Kavanagh, N Dunne.
Subs.: L Kelly for Mullally (46), W Mulhall (0-1) for B Allen (50), J O’Connor for Crombie (51), D Kelly for Dunne (60), J Evans for Bracken (65), C McNamee for R Allen (69).
Referee: P Maguire (Longford).