Full-forward David Maye was the hero for Sligo with some superb free-taking, while sub James Hynes crowned a great performance when introduced with some fine points. Galway were in trouble when they led by just 0-6 to 0-5 at the break having played with the strong wind in the first half at Tuam Stadium.
Sligo goalkeeper Brian McGovern produced a stunning save when he dived low to his left to save a penalty from Michael Martin after 19 minutes after Danny Cummins was fouled. At the time Galway were leading by 0-4 to 0-3 but Sligo hit back and Maye kicked another good free into the wind to level the match.
Captain Paul Conroy and centre-forward Tommy Walsh were the only Galway players to score from play with the wind, with Paul Kelly and Niall Judge responding for Sligo.
Galway hit three points without reply in the opening five minutes of the second half but Sligo took over from there and Alan Dunne and Maye were on target to reduce the deficit to 0-9 to 0-7 going into the final quarter. Maye left just one between them with nine minutes remaining before James Clarke levelled with a superb point from 45 yards.
Maye edged Sligo in front four minutes from time but Jonathan Ryan forced the game into extra-time two minutes from the end on a scoreline of 0-10 each.
Sligo laid down a big marker when points from Maye and Hynes saw them lead by 0-12 to 0-10 at the end of the first period of extra-time even though they were playing against the wind.
Hynes extended the lead to a goal shortly after the restart and while subs Rory Gaffney and Pat Mark O Fatharta found the range for Galway, Sligo deservedly held out for victory.
Scorers for Sligo: David Maye (0-7, 6f); J Hynes (0-2); P Kelly (0-1); N Judge (0-1); A Dunne (0-1); J Clarke (0-1).
Scorers for Galway: P Conroy (0-3, 2f); M Martin (0-3, two frees); T Walsh (0-1); D Cummins (0-1); J Ryan (0-1); E Monahan (0-1); R Gaffney (0-1); P O Fatharta (0-1, free).
SLIGO: B McGovern; J Kelly, G Gilsenan, V Gaughan; R McGarigle, B O’Boyle, K Cawley; C Davey, C Burns; P Kelly, P Clarke, D Gilsenan; N Judge, David Maye, A Dunne.
Subs: Daniel Maye for J Kelly, (25); J Clarke for Davey, (49); C Brady for P Clarke, (50); J Hynes for P Kelly, (54); P Greene for Burns, (60).
GALWAY: B Power; J Duane, C Forde, K Kelly; C Doherty, D Reilly, G Sweeney; P Conroy, JJ Greaney; M Boyle, T Walsh, J O’Brien; E Monaghan, M Martin, D Cummins.
Subs: J Ryan for Boyle, (45); R Gaffney for Walsh, (57); P O Fatharta for O’Brien, (60); C Halloran for Monahan, (71); A Griffin for Greaney, (78).
Referee: V Neary (Mayo).