Second half goals from Seán Bugler and Con O'Callaghan were the difference at Pearse Stadium on Sunday afternoon as Dublin inflicted Galway's second defeat in as many games.
The Tribesmen surrendered a two point lead at half-time as Dublin outscored the hosts by 2-7 to 0-6 in the second period.
Paul Conroy top scored for Pádraic Joyce's men with eight points, six coming from frees.
The defeat sees Galway finish a disappointing third in the Allianz Football League Division 1 after they had won four of their opening five matches.
After winning the toss, Galway decided to play with a strong wind at their backs but despite the environmental advantage, it was the visitors who troubled the scorekeepers first as Dean Rock slotted a free after two minutes.
Centre half forward Paul Conroy then responded with a free of his own before hitting a sumptuous score from the side line to put the Tribesmen ahead after four minutes.
Rock and Conroy then traded points before Ciaran Kilkenny's effort on the 16th minute mark tied the sides up before the drinks' break.
Galway were reenergised by the small interval as they reeled off four of the next five scores to take a three point lead after 23 minutes.
However, the All-Ireland champions were not going to allow the home side to pull away from them and in the second quarter of the first period, points from Paddy Small, Con O'Callaghan, and another free from Rock, brought the sides level just after the half hour mark.
With the minutes ticking down until the half-time whistle, Galway managed to get their noses in front thanks to the metronomic kicking of Conroy who had his fifth and sixth point of the day via two frees.
Facing into the wind, the home side began the second period strongly with points from sub Shane Walsh, Gary O'Donnell, and another free from Conroy, opening up a four point gap, however, that was as good as it was going to get for Galway as Dublin hit 1-4 in the space of nine second half minutes to take control of the contest.
The sides continued to trade scores before O'Callaghan raised the green flag in the third minute of added on time to extinguish any hope of Galway stealing an unlikely victory.
Galway: P Conroy 0-8 (6f ); R Finnerty 0-2 (1f ); A Varley 0-1; S Walsh 0-1; G O'Donnell 0-1; J Leonard 0-1; L Silke 0-1.
Dublin: D Rock 0-6 (4f ); S Bulger 1-1; P Small 0-4; C Kilkenny 0-2; C O'Callaghan 1-2;
Galway: Bernard Power; Sean Kelly, Sean Mulkerrin, James Foley; Liam Silke, Gary O'Donnell, Johnny Heaney (c ); Cein D'Arcy, Tom Flynn; Paul Kelly, Paul Conroy, Jason Leonard; Robert Finnerty, Adrian Varley, Ian Burke.
Subs: M Barrett for Flynn (32 ); S Walsh for Burke (HT ); G Sice for Finnerty (HT ); C McDaid for O'Donnell (54 ); G Bradshaw for P Kelly (59 ).
Dublin: Stephen Cluxton; Cian Murphy, David Byrne, Michael Fitzsimond; John Small, Jonny Cooper, Robert McDaid; Brian Fenton, Emmet Ó Conghaile; Eric Lowndes, Ciaran Kilkenny, Niall Scully; Paddy Small, Con O'Callaghan, Dean Rock.
Subs: S Bugler for Lowndes (HT ); C Costello for McCarthy (46 ); T Lahiff for Howard (62 ); K McManamon for P Small (68 ); P McMahon for Murphy (73 ).
Referee: David Coldrick (Meath ).