Tipperary recorded their first win in the Munster Championship since 2003, with Peter Creedon's side winning by 2-14 to 1-11 at the Gaelic Grounds.
An early goal from Barry Grogan set Tipperary on their way and by half-time they enjoyed a 1-07 to 0-06 lead.
Tipperary came out and blitzed their hosts in the opening part of the second-half, with Philip Austin grabbing their second goal.
An opportunity for a third goal was spurned, when Grogan had a penalty saved, following a fould on Ian Fahey.
However, by that stage Tipperary led by 2-09 to 0-07, and, despite Limerick scoring a penalty through Eoin Hanrahan and pushing their visitors hard in the final stages, they ran out winners to advance to the semi-finals.