Goals in the second-half from Sean Bugler and Con O’Callaghan sealed the win against the Tribesmen, who were much improved from the side hammered by Mayo a week earlier.
The sides exchanged three points in the opening half as Galway tried to build a lead, having opted to play with the strong wind into the town goal.
Long-serving Paul Conroy delivered all three for the Tribesmen, his first from a free and then two excellent points from distance from play.
Dublin played a good possession game into the elements and after Dean Rock responded to each of Conroy’s efforts, Ciaran Kilkenny levelled at the end of the third quarter after a good build-up.
Galway pulled two clear for the first time thanks to points from Adrian Varley and Rob Finnerty after 19 minutes.
And while Paddy Small pulled back the deficit with an excellent score from the right, Galway opened up a goal lead with further points from Finnerty and Conroy.
Dublin kept their composure and were patient building moves. Paddy Small got another fine point and Con O’Callaghan and Rock struck to level the match.
However, Galway went in leading by 0-9 to 0-7 at the interval when Conroy hit two more frees.
Galway, having introduced captain Shane Walsh and the experienced Gary Sice at the break, extended the lead to 0-12 to 0-8 after 46 minutes but then Paddy Small and Rock landed points before sub Sean Bugler blasted to the net and quickly added a point to lead by 1-11 to 0-12 going into the final quarter.
The impressive Paddy Small got his second point from a mark to take his tally to four and extend the lead to a goal before Jason Leonard cut the gap to two with seven minutes remaining.
Dublin never looked like letting it slip in the closing stages and they wrapped it up when O’Callaghan drilled low to the net after a fisted effort for a point came back off the right upright and he made no mistake with the rebound.
C O’Callaghan 1-2 (1m), D Rock 0-6 (4f), P Small 0-4 (2m), S Bugler 1-1, C Kilkenny 0-2.
P Conroy 0-8 (6f), R Finnerty 0-2 (1f), S Walsh 0-1, A Varley 0-1 (m) G O’Donnell 0-1, L Silke 0-1, J Leonard 0-1.
S Cluxton; C Murphy, D Byrne, M Fitzsimons; E Murchan, J Small, R McDaid; B Fenton, J McCarthy; B Howard, E Lowndes, C Kilkenny; P Small, C O’Callaghan, D Rock.
S Bugler for Downes (ht), C Costello for McCarthy (46), T Lahiff for Howard (63), K McManamon for P Small (68), P McMahon for Murphy (70).
B Power; S Mulkerrin, S Kelly, J Foley; L Silke, G O’Donnell, J Heaney; C D’Arcy, T Flynn; P Kelly, P Conroy, J Leonard; R Finnerty, A Varley, I Burke.
M Barrett for Flynn (31), S Walsh for Burke (ht), G Sice for Finnerty (ht), C McDaid for O’Donnell (53), G Bradshaw for P Kelly (59).
David Coldrick (Meath).
