A Paudie O'Sullivan goal ten minutes from time clinched a draw for Cork at Pearse Stadium, as Galway remain at the foot of the Allianz Hurling League Division 1A table with one game remaining.
Cork led by 1-7 to 1-6 at half-time after goals from Davy Glennon for the home side and an Anthony Nash penalty.
Galway looked in total control when Cyril Donnellan hit the net from close range in the 51st minute, but O'Sullivan's goal and two frees from Cian McCarthy earned the Rebels a share of the spoils.
Galway looked lively early on as Joe Canning hit an early free and a point from play to give his side an early cushion.
But Jimmy Barry-Murphy's side went on to hit four of the next five points as Patrick Hogan, Paudie O'Sullivan, and the very impressive Lorcan McLoughlin all got in on the act.
However, after they had edged ahead 0-04 to 0-03, Cork were struck with a severe blow when Glennon goaled for the Tribesmen in the 21st minute, with his crisp, low shot leaving Anthony Nash with no chance.
McLoughlin hit a lovely point over his shoulder to reignite the Cork challenge, but with his injury and suspension woes behind him, Donnellan hit a sweet point of his own from the right wing to give Galway the two point lead once again.
A pair of Canning frees gave Galway a decent lead approaching the break, but Nash crashed a penalty past Colm Callanan after Fergal Moore was harshly adjudged to have fouled Luke O'Farrell a minute from the break.
Donnellan and Canning had edged Galway ahead again by the 50th minute and a minute later the Tribesmen looked in total control when Donnellan hit the net after he fielded an arrowed cross from Davy Glennon at the edge of the square.
But Cork were not to be denied at least a point from their trip to Salthill and after Cian McCarthy hit a free and substitute Stephen Moylan chased it with a good point from play, O'Sullivan hit the crucial score.
Galway: C Calanan; F Moore, K Hynes, J Coen; A Harte, D Collins, N Donoghue; I Tannian, A Smith; J Cooney, J Canning (0-10, 0-07f, 0-01sl), J Glynn; C Donnellan (1-02), D Hayes, D Glennon (1-00).
Subs: T Haran for Glennon (65), B Flaherty for Smith (68)
Cork: A Nash; S O'Neill, B Murphy, C O'Sullivan; C Joyce, P Cronin (0-01), W Egan (0-01); T Kenny, L McLoughlin (0-03); C Lehane (0-01), P O'Sullivan (1-01), S Harnedy; A Mannix, L O'Farrell (0-01), P Horgan (0-01, 0-01f).
Subs: C McCarthy (0-02, 0-02f) for Harnedy (h-t), M Cussen for Horgan (45), S Moylan (0-01) for Mannix (53), F O'Leary for Lehane (62), S White for Egan (65).