Galway produced a superb display in the second-half to book a quarter-final showdown with Wexford next weekend as they secured a deserved 3-21 to 3-13 win in the rain at Pearse Stadium.
Two goals from Conor Whelan and one from Cathal Mannion sent Shane O'Neill’s men on the way to victory.
Tipperary, with captain Seamus Callanan having decided to play with the wind, seemed to be in trouble when they only led by two points after half an hour.
But they finished the half strongly to lead by 3-07 to 0-09 at the break with Jason Forde finishing off a good move to score their third goal just before the interval.
John McGrath got their opening two goals, striking after just two and a half minutes for the opening score of the game after he collected a delivery from Alan Flynn to score.
Forde added a 65 shortly afterwards but Galway did not panic and Evan Niland, one of three changes before the start, hit three points in a row.
The Clarinbridge clubman had scored 0-08 by the break, landing all seven of his frees, with Brian Concannon getting Galway’s only other score of the opening half.
McGrath got his second goal from a tight angle after 21 minutes when the Galway defence failed to deal with a free from distance from Forde which dropped short.
Galway were in a good position five minutes from the break when Tipperary only led by 2-04 to 0-08, but they finished the half strongly.
Seamus Callanan, Ronan Maher and Cian Darcy shot points before Forde found the net after a neat move which involved Padraic Maher, Callanan and Darcy to leave them seven ahead at the interval.
Galway, backed by the bulk of the crowd of 5,750, came storming back after the break and got a huge boost when Whelan got the first of his goals after being set up by Concannon.
Tipperary kept in touch with points from Padraic Maher, Dillon Quirke, Michael Breen and Jason Forde and took a 3-11 to 1-14 lead into the final quarter.
But Galway took over from there and outscored them by 2-07 to 0-02 from there to the finish.
Jason Flynn pointed a superb sideline moments after being booked in a melee and while Cian Darcy responded for Tipperary, it was Galway who dominated from there to the finish.
Niland pointed another free and then a delivery from Johnny Coen saw Whelan get through for a superb goal to put Galway ahead for the first time in the game with 14 minutes left.
They pushed on from there with Niland pointing a couple of frees either side of another effort from the impressive Concannon as they pulled away.
They sealed the win and a quarter-final date with Wexford when Cathal Mannion soloed through to shoot home their third goal in the dying moments.
Galway: James Skehill; Darren Morrissey, Gearoid McInerney, Paul Killeen; Padraic Mannion, Shane Cooney, Fintan Burke; Johnny Coen (0-01), Aidan Harte; Cathal Mannion (1-00), Conor Whelan (2-00), Evan Niland (0-14, 0-13f); Conor Cooney (0-01), Jason Flynn (0-01, sideline), Brian Concannon (0-04).
Subs: Sean Loftus for Killeen (25), Adrian Tuohey for S Cooney (45), David Burke for P Mannion (56), Niall Burke for Flynn (56), Kevin Cooney for Concannon (66).
Tipperary: Brian Hogan; Paul Maher, Barry Heffernan, Ronan Maher (0-01); Seamus Kennedy, Padraic Maher (0-01), Alan Flynn; Noel McGrath, Ger Browne; Jason Forde (1-05, 0-02f, 0-02 ’65), Seamus Callanan (0-01), Dillon Quirke (0-01); John McGrath (2-01), John O’Dwyer, Cian Darcy.
Subs: Michael Breen (0-01) for Browne (48), Sean O’Brien for P Maher (48), Paul Flynn for O’Dwyer (57), Dan McCormack for Quirke (59), Jerome Cahill for Darcy (69).
Referee: Johnny Murphy (Limerick).