Damien Comer hit 1-2 in the second half as Galway produced a strong second half to overpower Fermanagh at Brewster Park.
The visitors trailed by 0-7 to 0-3 at half time, Fermanagh worthy leaders despite the early loss of skipper Eoin Donnelly to a black card.
The bitterly cold wind probably should have favoured Fermanagh in the second half, but was all Galway after Comer gave the perfect start with a goal 10 seconds after the throw-in.
After a quiet first half, himself and Paul Conroy were the influential figures in the comeback in what was a valuable away win for the promotion hopefuls in Division Two of the Allianz Football League.
Despite the loss of their leader Donnelly, Eddie Courtney showed well inside and clipped over the first of his two first-half points.
Galway won several Femanagh kickouts in a row in a good little spell and drew level through Michael Daly and a long-range effort from Conroy.
From three points all, Fermanagh took over in the 10 minutes before half time with four points in a row, three from Sean Quigley. His '45', a long-range and a point to leave Fermanagh in a good place heading into the second half.
But Galway manager Kevin Walsh's half-time team-talk stirred his players and they were a different side after the throw-in.
Comer had the ball in the back of the net after just 10 seconds to undo most of Fermanagh's good first-half work.
Galway won the throw-in and in a flash, Comer's shot across goal planted into the far corner.
Fermanagh tried to keep their noses in front as long as possible and Barry Mulrone scored a neat point from the wing, and Corrigan again edged them ahead after Galway drew level, but the tide was turning.
Two successive points from Michael Daly put them ahead for the first time, at 1-7 to 0-9 in the 54th minute.
They kicked strongly for home, with Barry McHugh nailing three frees into a tricky wind and Conroy winning a kickout, running through and clipping it over the bar.
Galway outscoring the home side by 1-10 to 0-3 in a one-sided second half.
Erne cornerback Cian McManus was sent off following a foul on Gareth Bradshaw near the end, but it was irrelevant to the result.
Scorers for Fermanagh: Sean Quigley 0-3 (1f, 145), Tomas Corrigan 0-2 (1f), Eddie Courtney 0-2, Barry Mulrone, Lee Cullen, Aidan Breen 0-1 each.
Scorers for Galway: Damien Comer 1-2, Barry McHugh 0-4 (4fs), Michael Daly 0-3, Paul Conroy 0-2, Thomas Flynn, Eamonn Brannigan 0-1 each.
FERMANAGH: Chris Snow; Patrick Rehill, Che Cullen, Cian McManus; Declan McCusker, Ryan McCluskey, Barry Mulrone; Eoin Donnelly, Lee Cullen; Aidan Breen, Cathal Beacom, Paul McCusker; Eddie Courtney, Sean Quigley, Tomas Corrigan.
Subs: Ryan Lyons for Donnelly (BC, 9), Ciaran Corrigan for Beacom (HT).
GALWAY: Rory Lavelle; Declan Kyne, David Walsh, Luke Burke; Gary O'Donnell, Gareth Bradshaw, Johnny Heaney; Paul Conroy, Fiontan O Curraoin; Thomas Flynn, Damien Comer, Michael Daly; Cillian McDaid, Barry McHugh, Sean Armstrong.
Subs: Eamonn Brannigan for Armstrong (41), Sean Kelly for McDaid (42), Enda Tierney for McDaid (70), Cathal Sweeney for McHugh (70).
REFEREE: Jerome Henry (Mayo).