Tipperary manager Eamon O'Shea admitted his side could easily have lost to Cork and attributed their come-from-behind one-point win to the players' belief and never-say-die attitude.
The Premier county trailed their Munster rivals by four goals at one stage of the second half at Pairc Ui Rinn but recovered to win by 2-28 to 4-21 thanks to Noel McGrath's late point.
"The team kept believing that they could do something and once you keep believing...," he told RTÉ Sport.
"We were probably lucky in the end to get the win. Both teams played well at various stages of the game but we played well at the end I suppose. It was a good game."
Tipperary have lost two league finals and an All-Ireland final to Kilkenny since O'Shea took over for the 2013 season, and he hinted that the pain of those defeats helped to forge the belief the team showed on Leeside.
"We've been through quite a bit, this team, over the past 18 months, both good and bad," he said.
"You get a certain amount of maturity and belief when you have to deal with adversity and the team is showing some signs of that, I hope."
O'Shea played down the notion that Sunday's victory, added to last year's All-Ireland semi-final thrashing of Cork, gives his team a psychological edge over their neighbours.
"I don't know if you can take things like that from it," he said.
"They could have won this game by 12 at various stages but we just kept believing. Every game has to be taken as what it is, a new game."
As Division 1A winners and top seeds, Tipperary will play Division 1B's fourth-placed team Offaly, in the quarter-finals.
"Offaly will be a hard test," said O'Shea. "We got a hard test off them in the qualifiers last year and I expect a good, solid game."
