Galway manager Cathal Murray says their experience was crucial as they came back to see off Waterford at Thurles on Saturday evening.
The Tribeswoman were a goal behind with the first score of the game, but they hit right back through Beth Carton.
The Déise still took a four point lead into the break. From there though, Galway got on top, and went on to win by eight points.
'That was one tough game' - Galway's player of the match Ailish O'Reilly says experience helped them get past Waterford in Semple Stadium today. pic.twitter.com/V3HmWAmyrn— The Sunday Game (@TheSundayGame) August 3, 2019
"We had to weather a serious storm," Murray told RTÉ Sport's Marie Crowe.
"They're a fiece physical team. In the first-half they won all the battles, to be honest with you.
"We re-set at half-time, and the second-half performance was excellent. Look, it's not going to be good enough to bother Cork, but the prize today was always to be in the semi-final after the game.
"The performance mightn't have been what we wanted, but the second-half was super and we're delighted to win it."
The Littlewoods Ireland League champions were drawn against Cork in the semi-final, with Kilkenny and Tipperary set to clash on the other side.
Murray says they don't fear anyone, as they look to reach the final for the first time in four years.
"At different times this year, things haven't been going for us," he admitted.
"But we stuck with it. We stayed working hard, and doing the right things. And when we play really, really well, which we did in the second-half, we can do damage.
"Anytime we got ball into Ailish O'Reilly or Noreen Coen in the full-forward line, they looked really dangerous.
"We're used to that, we're used to winning quarter-finals I suppose, and we have to carry that on to two weeks time."