Young substitute Declan McLoughlin landed a splendid late point, deep into stoppage time, to ensure the Leinster SHC spoils were divided.
Galway struck three points in a row in the closing stages to deny an Eoin Cody inspired Kilkenny outfit.
Cody was in brilliant form for the Cats, mining six points from play, causing the Tribesmen significant bother throughout.
At the opposite end of the field Brian Concannon was similarly effective for Galway, who pounced for a sixth minute goal.
That was supplied by Concannon, who gathered a Jack Grealish delivery before rattling the Kilkenny net. Galway led 1-3 to 0-4 at that stage with the opening period providing plenty of scores.
John Donnelly and Cody were effective for Derek Lyng's charges, who subsequently hit the front as the interval approached.
A couple of points, though, from Evan Niland ensured the teams departed deadlocked, 0-16 to 1-13 at the interval.
After the restart Kilkenny enjoyed a productive spell with Billy Ryan, TJ Reid, Cody, and Adrian Mullen clipping neat points for the black and amber side, who led 0-26 to 1-18 with just over 13 minutes remaining.
Galway remained defiant with replacements Jason Flynn, Liam Collins, and Declan McLoughlin all rifling over important scores in the closing stages.
Scorers for Kilkenny: TJ Reid 0-9 (8fs ), Eoin Cody 0-6, Darragh Corcoran, Adrian Mullen, John Donnelly, Billy Ryan, and Martin Keoghan 0-2 each, Mikey Butler, Timmy Clifford, and David Blanchfield 0-1 each.
Scorers for Galway: Brian Concannon 1-5, Evan Niland 0-7 (6fs ), Conor Whelan 0-2, Padraic Mannion, Daithi Burke, Joseph Cooney, Cianan Fahy, Ronan Glennon, Cathal Mannion, Kevin Cooney, Conor Cooney, Jason Flynn, Liam Collins, and Declan McLoughlin 0-1 each.
Kilkenny: Eoin Murphy; Mikey Butler, Huw Lawlor, Tommy Walsh; David Blanchfield, Richie Reid, Padraig Walsh; Darragh Corcoran, Conor Fogarty; Timmy Clifford, Adrian Mullen, John Donnelly; Billy Ryan, TJ Reid, Eoin Cody.
Subs: Martin Keoghan for Clifford (HT ), Cian Kenny for P Walsh (46 ), Alan Murphy for Donnelly (65 ), Cillian Buckley for Fogarty (70+3 ).
Galway: Eanna Murphy; Jack Grealish, Gearoid McInerney, TJ Brennan; Padraic Mannion, Daithi Burke, Joseph Cooney; Cianan Fahy, Ronan Glennon; Cathal Mannion, Conor Cooney, Kevin Cooney; Conor Whelan, Brian Concannon, Evan Niland.
Subs: Jason Flynn for C Cooney (58 ), Fintan Burke for Glennon (60 ), Liam Collins for Fahy (65 ), Declan McLoughlin for Whelan (68 ).
Referee: J Murphy (Limerick ).
