Conor Cooney was the Galway hero when he landed a free from distance on the right to snatch victory in the final play of a thriller in Salthill as Henry Shefflin got the bragging rights over his old mentor Brian Cody.
Kilkenny struck for an equalising goal in the third minute of injury-time but Cooney kept his nerve to land the winner.
There was a tense handshake afterwards as Shefflin went to commiserate with Cody, with the Kilkenny manager clearly unhappy with referee Colm Lyons after a dramatic contest.
The sides were level four times in the opening half but Galway went in leading by 1-17 to 2-08 after a frenetic opening half.
Kilkenny captain Eoin Cody opted to play against the wind in the opening half and Galway came out of the blocks shooting three points in the opening two minutes with brothers Pádraic and Cathal Mannion finding their range along with their cousin Brian Concannon.
Pádraig Walsh settled Kilkenny with a point and then Cody, a nephew of Galway manager Shefflin, pointed before he fired home the opening goal following a good run from Walter Walsh to lead by 1-02 to 0-03 after just six minutes.
Galway got back on level terms after 12 minutes when Conor Cooney pointed a long-range free and efforts from Cianan Fahy and Joseph Cooney edged them in front.
TJ Reid, who missed two frees in the opening half, found the range from 60 metres before Billy Ryan shot home their second goal after 16 minutes after a good pass from Cody.
But with Galway executing multiple turnovers, they pulled away with Tom Monaghan and Joseph Cooney both shooting three points from play by the break, with the Tribesmen hitting 1-10 from turnovers before the interval.
A couple of Reid points after his goalkeeper Eoin Murphy had caved from Fahy, edged Kilkenny 2-7 to 0-12 in front after 22 minutes but then Galway found top gear and struck for 1-05 without reply in a blistering ten-minute spell.
Johnny Coen, a late replacement for Evan Niland, drilled home the goal after a turnover from Fahy and a pass from Concannon and points followed with two apiece from Monaghan and Joseph Cooney, while Cathal Mannion picked off his second of the afternoon.
Adrian Mullen pulled back the margin to six points when he scored from the right to leave it 1-17 to 2-08 at the interval.
Conor Cooney extended the lead with his fourth free of the game a minute after the restart but Kilkenny, who replaced TJ Reid at the break with Tom Phelan, took over and landed the next seven points without reply in a blistering period of fast hurling with Walter Walsh very effective as the sides were level for a fifth time in the game.
Galway weathered the storm well and struck the next three points to lead by 1-21 to 2-15 after 59 minutes before Alan Murphy got his fourth point of the half with his third free.
But Conor Cooney restored the goal lead with seven minutes remaining and after Murphy and Concannon exchanged points, that was the gap between the sides going into three minutes of stoppage time.
Then Kilkenny struck after 73 minutes when Cody set up sub John Donnelly and his shot found the net to tie the sides.
But there was still time for more drama when Monaghan was fouled by Paddy Deegan and Cooney kept his nerve to steer the winner from 65 metres on the right in the 75th minute of a gripping contest.
Galway: Eanna Murphy; Darren Morrissey, Daithi Burke, Jack Grealish; Pádraic Mannion (0-01), Gearóid McInerney, Fintan Burke (0-02sl); David Burke (0-01), Johnny Coen (1-00); Tom Monaghan (0-03), Conor Cooney (0-06f), Joseph Cooney (0-04); Cathal Mannion (0-02), Brian Concannon (0-04), Cianan Fahy (0-01).
Subs: Tiernan Killeen for Grealish (41-43 blood), Conor Whelan for Fahy (45), Gavin Lee for Grealish (52), TJ Brennan for Coen (72).
Kilkenny: Eoin Murphy; Mikey Butler, Huw Lawlor, Tommy Walsh; Mikey Carey (0-01), Paddy Deegan, Conor Browne; James Maher, Adrian Mullen (0-01); Cillian Buckley, Pádraig Walsh (0-02), TJ Reid (0-03, 2f); Walter Walsh (0-03), Billy Ryan (1-00), Eoin Cody (1-02).
Subs: Alan Murphy (0-05, 1f) for Maher (31), Tom Phelan for Reid (half-time), David Blanchfield for Browne (42), John Donnelly (1-00) for Buckley (55), Martin Keoghan for Ryan (66).
Referee: Colm Lyons (Cork).
