They overturned a two point deficit at the break to win by 3-25 to 4-19 in their quarter-final clash at Semple Stadium.
Goals in the first seven minutes from Denis Maher and Niall O' Meara saw Tipperary blaze into a 2-04 to 0-00 lead.
However, Cork fought back and went in at half-time leading by 3-11 to 3-09.
But Eamon O' Shea's men eventually prevailed, ith John O' Dwyer scoring 1-07, and will now face the All-Ireland champions on April 20th.
And it was a great day all round for the Tipperary teams, with Peter Creedon's senior footballers securing promotion to Division 3 of the Allianz Football League.
Goals from Brian Fox, Philip Austin and Ian Fahey- plus a brace from Conor Sweeney- saw them beat Leitrim by 5-16 to 0-16 in their Division 4 clash at Pairc Sean MacDiarmada.
Elsewhere, Tipperary's Ladies football team defeated Longford by 0-15 to 1-07 in their Division 3 League game, while Tipperary's Minor camogie team have advanced to the All-Ireland Semi-Finals, following their 2-07 to 0-07 win against Wexford.
