Galway defeated Brian Boyle's side in a keenly fought Group 2 encounter in Athenry.
The Tribeswomen led 1-7 to 1-6 at the break – Tipp's goal was scored by Orla O'Dwyer.
It was nip and nuck in the second period too with a point from Jenny Grace leaving just one between the side in the closing minutes of the match.
However, the home side rallied and points from Aoife Donoghue and Niamh McGrath saw them home.
Tipperary's next match is against Derry.
