Brian Boyle's side went down 2-14 to 1-12 in a match played at Carrignore WIT.
The Premier led 1-9 to 0-7 at the break, thanks, in part, to Megan Ryan's 12th minute.
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Tipp could have been further ahead if Róisín Howard's effort shortly after the green flag was raised for the first time during the game had gone under rather than just over the crossbar.
Cork put in a much better display in the second-half and goals from Katrina Mackey and Niamh McCarthy helped them to a five-point victory.
Tipperary's next match is away to Wexford on Sunday week, March 12th.
