Tipperary 3-13 Galway 1-10
Michael Quinlivan and Conor Sweeney combined in stunning fashion at Croke Park to send Championship surprise packets Tipperary through to the All-Ireland semi-finals for the first time since 1935.
The duo blasted 3-06 between them with Quinlivan's early goal putting the Munster men into a lead they wouldn't relinquish, while Sweeney secured the success with two second-half goals.
Kevin O'Halloran contributed four points from frees also, though it was a fine all round performance from Liam Kearns' side who will meet Tyrone or Mayo in the last four on August 21 back at Croke Park.
On this sort of form, they will fancy their chances of making a final and perhaps becoming Gaelic football's answer to Premier league soccer champions Leicester City.
But it's the end of the line for Galway who had high hopes for the All-Ireland series after regaining the Connacht title with a memorable win along the way over Mayo.
They were no match for Tipp's pace and power and the Premier County's win is all the more impressive considering the 11 players they lost for various reasons after last year's Championship.
Tipp took no negative vibes into the contest despite watching fellow first time quarter-finalists Clare receive a sound beating from Kerry in the earlier game.
Their heads still didn't drop after falling 0-04 to 0-01 down after 15 minutes either following Galway points from Danny Cummins, Shane Walsh and Eamon Brannigan.
In fact, it only seemed to spur them into action and they opened up with some exciting attacking football that displayed their full range of skills from there on.
In all, Tipp hit with 1-06 without reply between the 15th and 33rd minutes as the Galway defence found itself under siege.
It was thrilling from Tipp and Quinlivan in particular, whose 17th minute goal when he palmed in from close range after good work by Robbie Kiely and George Hannigan was the spark.
Quinlivan added two points before free-taker O'Halloran opened his account and Sweeney then got in on the act.
Tipp led 1-07 to 0-04 approaching the break but Galway hauled themselves back into the contest with a brilliant Damien Comer goal.
He raced onto Paul Conroy's pass and powered past Alan Campbell before blasting to the net, leaving Tipp just 1-08 to 1-05 up the interval.
Galway's defence was always vulnerable though and Tipp exposed it time and again in the second-half as they soared to a famous win.
Quinlivan and Philip Austin both had goal chances though Sweeney wasn't to be denied and netted in the 38th and 47th minutes to put the Premier into a spectacular 10-point lead.
Bill Maher did the spade work for the first goal, playing in Sweeney after a solo run through the middle and Sweeney got his fist to Jimmy Feehan's long ball for the second.
Tipp could afford to drop down a gear in the closing 20 minutes or so and still beat Galway with nine points to spare.
The Tribesmen only managed two points from play in the entire second-half and both of those scores came in the last 10 minutes on a day of regrets for Kevin Walsh's outfit.
Tipperary: E Comerford; C McDonald, A Campbell, C O'Shaughnessy; B Maher, R Kiely (0-01), J Feehan; P Acheson (0-01), G Hannigan; J Keane, K O'Halloran (0-04, 0-02f, 0-01 45), B Fox (0-01); P Austin, M Quinlivan (1-04, 0-01f), C Sweeney (2-02).
Subs: A Moloney for Keane, S Leahy for Maher, M Dunne for Hannigan, M Hanley for Quinlivan.
Galway: B Power; E Kerin, D Kyne, D Wynne; L Silke, G O'Donnell, G Bradshaw; P Conroy (0-01), T Flynn; G Sice, J Heaney, E Brannigan (0-01); D Cummins (0-03), S Walsh (0-04, 0-04f), D Comer (1-00).
Subs: A Varley for Sice, P Varley (0-01) for Heaney, E Tierney for Brannigan, P Sweeney for A Varley, P Cooke for Walsh, E Hoare for Conroy (BC).
Referee: C Lane (Cork)