A penalty shootout was required to separate arch rivals Galway and Mayo but with goalkeeper Maghnus Breathnach superb, it was the Tribesmen who advanced.
Galway had to come from behind in injury-time with a goal from Barry McHugh forcing the shooutout.
Galway then advanced when Liam Silke, Johnny Heaney, McHugh and Tom Flynn found the net after their goalkeeper Maghnus Breathnach saved efforts from Diarmuid O’Connor and Andy Moran, with Brian Reape and James Kelly converting their kicks.
Mayo led by 1-5 to 0-3 at the break, with Jason Doherty getting the goal five minutes from the interval after a long ball by Michael Plunkett.
Galway did not score from play in the opening half against the wind, with Mayo full-forward Brian Reape again impressing, shooting 0-3 from play during the contest at Tuam Stadium.
Doherty and McHugh twice exchanged points early in the second-half to leave it 1-7 to 0-5 after 46 minutes.
Galway got the gap down to a goal after 58 minutes after Johnny Heaney had hit the post when McHugh pointed a 45 but almost immediately Reape hit back with his third point of the afternoon.
However, Galway did not give up and McHugh saved them with his late goal before goalkeeper Breathnach saved the efforts from O’Connor and Moran.
Reape and James Kelly found the net for Mayo but Galway advanced to the final as Liam Silke, Heaney, McHugh and Tom Flynn hit the target to set up a clash with Roscommon next Sunday.
Armagh beat Donegal by 0-14 to 1-10 in Omagh, while Tyrone got the better of Derry on a scoreline of 0-14 to 1-8.
Scorers for Galway: B McHugh 1-6 (4f, 1 ’45), J Daly 0-2 (1f), M Daly 0-1.
Mayo: R Hennelly; K Higgins, B Harrison, D Drake; C Boyle, M Plunkett, J McCormack; D Vaughan, D O’Connor; F McDonagh, C Loftus, F Boland; C Diskin, B Reape, J Doherty.
Subs for Mayo: A Moran for Loftus (35), C O’Shea for Boland (48), S Coen for McCormack (53), L Keegan for Doherty (64), J Kelly for Drake (72).
Galway: M Breathnach; D Kyne, S A Ó Ceallaigh, L Silke; K Molloy, J Daly, D Wall; K Duggan, T Flynn; C McDaid, M Farragher, J Heaney; F Burke, M Boyle, B McHugh.
Subs for Galway: P Cooke for Duggan (35), S Kelly for Molloy (42), M Daly for Farragher (50), G O’Donnell for Wall (52), E Kerin for J Daly (61).