Galway’s devastated players could not believe they had lost this thrilling contest, and it will be of little consolation to them that they contributed so generously to an epic quarter-final at Croke Park.

This was a game that had everything – six goals, limitless passion, courage and skill, and a lead that changed hands minute by minute.

The Tribesmen thought they had it as they headed for the finish with a two points lead, but Tipp hit the last three points of the game to take the glory from an unforgettable afternoon at GAA headquarters.

Tipp eased ahead in the early stages with points from Patrick Maher, Lar Corbett and Eoin Kelly (2), but they were rocked by a Galway goal in the 10th minute, Eanna Ryan’s pace carrying them through a hesitant defence for a superb solo strike.

Damien Hayes eased Galway in front for the first time on 13 minutes, and Joe Canning brought the sides level for the third time from a ’65 midway through the first half.

Tipperary immediately struck for a goal, Kelly collecting Maher’s knock-down to fire home a superb finish.

However, it was Galway who gained a fresh impetus from that score, scoring the next six points to go three clear.

Canning failed to score from play in the first half, chiefly through to the combined efforts of Paddy Stapleton, Paul Curran and Michael Cahill, but he converted superbly from a sideline cut, and tagged on a couple of frees.

Damien Hayes, Iarla Tannion and Ger Farragher, with a huge effort, were also on target as the Tribesmen made it six points on the spin, while solid defending from Tony Og Regan, Shane Kavanagh and David Collins kept Tipp scoreless for 16 minutes.

But Liam Sheedy’s men finished the half with a 1-2 salvo to take a four points advantage into the break.

Kelly and Brendan Maher knocked over points, before Noel McGrath’s flick sent substitute Seamus Callanan through for a stoppage time goal and a 2-8 to 1-9 lead.

Galway hit the front again with a sensational start to the second half.

Damien Hayes took advantage of a rare Paul Curran error to get in for a goal, and points from Farragher and Canning made it 2-11 to 2-10.

This remarkable tie quickly then took yet another twist, with Gearoid Ryan showing lightning pace to dart through for Tipp’s third goal on 43 minutes.

Corbett gave them the relative comfort of a four-point lead, but inevitably there was to be yet another goal.

Joe Canning was fouled and smashed home the penalty himself, and when Damien Hayes and Kevin Hynes tagged on points, the Connacht men were back in front with the scent of victory in their nostrils.

Hynes and fellow sub Aengus Callanan added further points, but Tipperary refused to surrender, and late scores from John O’Brien, Ryan and Corbett saw them win a classic contest.

Tipperary: B Cummins, P Stapleton, P Curran, M Cahill, D Fanning, C O'Mahony, P Maher, B Maher (0-2), D Young, G Ryan (1-2), P Maher (0-1), S McGrath, N McGrath (0-1), L Corbett (0-3), E Kelly (1-7 (0-6f).

Subs: S Callanan (1-0) for Young, J O’Brien (0-1) for N McGrath, C O’Brien for Fanning, P Bourke for P Maher

Galway: C Callanan, D Joyce, S Kavanagh, O Canning, D Barry, T Og Regan, D Collins, G Farragher (0-2), D Burke (0-1), E Ryan (1-1), K Hayes, A Smith, D Hayes (1-3), J Canning (1-5, 1-0 pen, 3f, 1s/l, 1 ’65), I Tannian (0-1).

Subs: K Hynes (0-2) for K Hayes, A Callanan (0-1) for Ryan, J Lee for O Canning.

Referee: J Owens (Wexford).