The Premier County beat Anthony Daly’s side 1-19 to 0-19 in Nenagh, while Kilkenny eased to victory over Wateford and Clare drew with Galway.
Dublin face a relegation play-off against the Déise after suffering a three-point defeat to Tipp.
The vistors actually led by the odd point in 19 – 0-10 to 0-09 – at the half-time break, with Alan McCrabbe prominent but a Seamus Callanan-inspired Tipperary were never far behind.
McCrabbe, Danny Sutcliffe and Ryan O’Dwyer helped Dublin to pull clear after the breat but Tipp clawed their way back with the only goal of the game through Patrick Bonner Maher.
Callanan and McCrabbe swapped a glut of scores close to the end but Tipperary proved victorious, with the Bonner Maher’s strike the crucial difference.
Kilkenny, meanwhile, showed no mercy to Wateford whatsoever in their 4-22 to 0-14 victory at Nowlan Park.
Brian Cody’s side rolled back the years as Jonjo Farrell’s goal helped them to a 1-07 to 0-08 lead at the break.
The second half, however, belonged to Kilkenny as further goals from Eoin Larkin and a Mark Kelly double helped Brian Cody’s side to an emphatic win.
Kilkenny will now face Wexford in the quarter-finals.
Finally, All-Ireland champions Clare grabbed a draw with Galway as Colin Ryan’s late free gave the Banner a 0-18 to 1-15 draw at Ennis.
Clare played much of the game with 14 men after Shane Golden was sent off for a clash with Iarla Tannion.
Cathal Mannion scored the only goal of the game for the Tribesmen after half-time, but Davy Fitzgerald refused to lie down and claimed a valuable draw.
