Substitute Shane Maloney pointed in the third minute of injury time to give Galway a 0-26 to 3-16 victory over Tipperary at Croke Park.
With 58,495 watching on in disbelief as a classic encounter unfolded, the sides were level ten times and Seamus Callanan culled an amazing 3-9 for the losers, but the westerners were not to be denied as last-gasp points from Jason Flynn and young debutant Maloney - who captained his county to minor glory four years ago and won an All-Ireland intermediate title last weekend - gave Anthony Cunningham's charges a deserved victory.
Galway will meet holders Kilkenny in the Liam MacCarthy Cup decider on September 6th.
Late points from David Burke, Cathal Mannion and Conor Whelan edged the victors into a 0-13 to 1-9 lead at the break, after the Munster champions had started like a house on fire.
With Callanan rampant on the edge of the square (notching 1-5 in the opening period), Tipp looked capable of pulling away but Galway readjusted well and registered eight of the last eleven scores before the short whistle.
Having won the toss, Tipp elected to play into Hill 16 in the first half, with the breeze behind them, and they got off to a dream start when Callanan collected a high deliver to drill the ball to the net after just 35 seconds.
The No.14 added a pointed free and Joe Canning opened Galway's account from a free on six minutes before seeing his penalty saved by Darren Gleeson three minutes later (after a foul on Cyril Donnellan).
Gleeson then denied Mannion and Canning missed the resultant '65' before Flynn fired over a second Galway score from distance. Callanan and Canning traded points, as did Jason Forde and Canning (free); John O'Dwyer pointed to leave three between them at the midway stage in the first half.
Callanan again took a pass from James Woodlock to make it double scores, 1-5 to 0-4, before cancelling out Canning's '65'; Flynn replied with his second and a simple Canning free closed the gap to two with eleven minutes left before the break.
Callanan's next point was replied to by Andy Smith and Brendan Maher swapped points with Mannion before Canning claimed his sixth score with a superb strike across the shoulder. An O'Dwyer free from inside his own half left two in it again with a minute left of regulation time in the first half.
Super strikes from midfielder Burke and Mannion drew the Tribesmen level and teenager Whelan clipped over the injury-time score that gave the westerners the narrowest of interval advantage. The men in maroon celebrated wildly when the half-time whistle sounded, although there was still another tough 35 minutes to play.
The first score of the second half came from a majestic Canning sideline cut into The Hill from the Hogan Stand side. Callanan drilled the ball to the net for the second time on 39 minutes after fielding another Rounte One delivery over Padraig Mannion, but Flynn replied instantly and Mannion edged the Tribesmen back in front with his third, 0-16 to 2-9.
After Callanan equalised from a free, Colm Callanan denied Patrick Bonnar Maher a third Tipp goal. The Galway keeper then thwarted O'Dwyer, while Gleeson saved from Canning. David Burke and Bonnar Maher traded scores; Mannion's fourth edged Galway back ahead on 50 minutes, 0-18 to 2-11.
Callanan equalised from a free and then completed his hat-trick of goals at the midway stage in the second half when he yet again gathered a high delivery before smashing to the net from a couple of yards. Back came Galway with points from Canning (two frees), Whelan and Jason Flynn (free) to lead once more with an hour played.
Callanan levelled from a '65' after his namesake had denied substitute Lar Corbett and the Tipp full forward then won a penalty, which he saw deflected over by Callanan for a point. Canning (free) equalised in the 66th minute. When sub Conor O'Mahony edged Tipp back in front, Mannion replied on 68 minutes.
Substitute Noel McGrath put Tipp back in front but there was one last twist as Galway levelled on 70 minutes through Flynn before Maloney settled it.
Galway - C Callanan; J Coen, J Hanbury, P Mannion; A Harte, I Tannian, Daithi Burke; A Smith (0-1), David Burke (0-2); C Whelan (0-2), C Donnellan, J Glynn; J Flynn (0-5, 1f), J Canning (0-10, 6f, 1'65, 1sl), C Mannion (0-5). Subs: J Cooney for C Donnellan, D Collins for A Smith, G Lally for A Harte, S Moloney (0-1) for J Cooney, P Brehony for J Hanbury.
Tipperary - D Gleeson; C Barrett, J Barry, C O'Brien; R Maher, Padraic Maher, K Bergin; J Woodlock, S McGrath; J Forde (0-1), B Maher (0-1), Patrick Maher (0-1); J O'Dwyer (0-2, 1f), S Callanan (3-9, 0-2f, 0-1pen, 0-1'65), N O'Meara. Subs: S Bourke for J Forde, N McGrath (0-1) for S Bourke, C O'Mahony (0-1) for J Woodlock, M Breen for R Maher.
Referee - B Kelly.