Joe Canning scored an astonishing winning point from the right sideline in the fifth minute of stoppage time to give Galway victory over Tipperay.
The dramatic late intervention gave the Tribesmen a 0-22 to 1-18 win in a keenly contested All-Ireland hurling semi-final at Croke Park on Sunday.
The sides were level 13 times but Canning's 11th point of the game sent the All-Ireland champions crashing out.
Galway will play the winners of next week's game between Cork and Waterford.
The final will be staged on 3 September.
John O'Dwyer had a chance to snatch an equaliser in the final play but his effort from the right tailed off and Galway's passage to the final was secured.
Galway may not have scored a goal for a third championship match in a row but their ability to pick off points when they were most needed saw them home.
It's the third year in a row that the All-Ireland semi-final has been decided by a single point between theses sides, with Galway gaining revenge for last year's loss.
Now they will fancy their chance of a first All-Ireland title since 1988 after surviving a thrilling conclusion.
The sides were level six times in the opening half but Tipperary, playing with the breeze, led by 1-10 to 0-12 at the interval.
The goal came after 24 minutes when John McGrath pounced on an error by Galway goalkeeper Colm Callanan and corner-back Adrian Tuohy to flick the ball to the net.
Galway: C Callanan; A Tuohy, Daithi Burke, J Hanbury; P Mannion (0-01, 0-01f), G McInerney, A Harte; J Coen (0-02), David Burke; C Mannion (0-01), J Canning (0-11, 0-06f, 0-01 sideline, 0-01 '65), J Cooney (0-01); C Whelan (0-04), N Burke, C Cooney (0-02).
Subs: J Flynn for N Burke (45), J Glynn for C Mannion (53), S Moloney for C Cooney (70), G Lally for McInerney (71-73).
Tipperary: D Gleeson; D Maher, J Barry, M Cahill; S Kennedy (0-01), R Maher, Paudie Maher (0-02); B Maher (0-03, 0-02f), M Breen; D McCormack, Patrick 'Bonner' Maher, N McGrath (0-02); J O'Dwyer (0-03), S Callanan (0-05, 0-03f), J McGrath (1-01).
Subs: S Curtin for Patrick 'Bonner Maher (7-10), J Forde (0-01) for Breen (34), N O'Meara for Forde (62).