The Galway hurlers have booked their place in the All-Ireland semi-finals.
The had just one point to spare over Cork following the opening quarter-final clash in Semple Stadium.
It finsihed Galway 2-19 1-21 Cork.
Jack Grealish and Conor Whelan hit the back of the net for the Tribesmen.
They will face reigning All-Ireland champions Limerick in the last four.