Galway blew Dublin apart in the second half of this play-off replay in Portlaoise as they ensured their Division 1A status for 2013 with a 4-21 to 0-19 victory.
A Joe Canning point separated the sides on a 1-11 to 0-13 half-time scoreline, with Canning also netting a 24th minute goal.
Paul Ryan (0-11) and Conor McCormack (0-03) kept Dublin in touch, but Galway went on to dominate with Canning, David Burke and Davy Glennon adding further goals late on.
Two points was the biggest gap between them for long spells of the opening half, as the sides swapped points on four occasions during a 13-minute period.
Quilty, Ryan and McCormack registered further points for Dublin, while Canning, Damien Hayes and Iarla Tannian kept Galway in touch.
The first real goal-scoring opportunity fell to last year's league champions, however Ryan's blazing 14th-minute shot was expertly blocked by Galway goalkeeper Fergal Flannery.
Ryan pointed a 65 to leave the scoreline at 0-08 to 0-06 after 22 minutes, before Galway hit back with the first goal of the game.
A Hayes shot came off the upright, breaking into the path of Davy Glennon who was duly fouled for a 21-metre free. Up stepped Canning to fire the ball into the back of the Dublin net.
The goal gave Anthony Cunningham's charges the lead for the first time, but Dublin continued to press hard for the remainder of the opening half.
The sides were level on four occasions in the closing 10 minutes of the half with Ryan and McCormack adding to their tallies, while captain John McCaffrey also claimed a fine point from play in the 29th minute.
Indeed Dublin could have been in front by the interval, but for a superb combined block by Galway stopper Flannery and centre-back Fergal Moore which kept out a McCormack shot.
David Burke and Glennon grabbed a point apiece as half-time loomed, and an injury-time point from Canning brought the Portumna clubman's tally to 1-03 and gave the Tribesmen a 1-11 to 0-13 buffer.
Canning claimed his fourth point on the restart, but thanks to scores from Ryan, just a point separated the sides in the 42nd minute.
However, Dublin's scoring opportunities dried up alarmingly in the second half, with all four points registered in the third quarter coming from Ryan's placed balls.
By that stage Galway had thundered ahead by 2-16 to 0-17. Playing some of their best hurling of the year to date, Hayes was the provider for a smashing second goal from Canning who sent a rasping shot to the net from 30 metres out.
For their third goal Canning had a shot initially blocked by Gary Maguire, but the Ballyboden custodian fumbled possession and Davy Glennon was on hand to finish off the chance.
Glennon's goal ensured a 3-16 to 0-17 lead and Galway showed no signs of easing up as points from Canning and David Burke left the Dubs 10 points adrift in the 58th minute.
Defender Joey Boland claimed a point back for a wilting Dublin side, but this was a rare score for his side as Galway continued to excel in all areas of the pitch with Hayes running strongly in attack.
Cyril Donnellan pointed before Niall Burke's 64th-minute goal sealed Dublin's fate. Daly's men battled on and substitute Daire Plunkett had a goal effort saved by the excellent Flannery.
Substitute Simon Lambert also had an injury-time penalty saved by the Padraig Pearses clubman as late points from Canning and Glennon confirmed an ultimately comfortable 14-point win.
The defeat comes as quite a setback for the Dubs who, just twelve months on from their historic Division 1 title success, have endured a fruitless league campaign that culminated in relegation.
SCORERS
Galway: J Canning 2-07 (1-06f), D Burke 1-04, D Glennon 1-02, N Burke 0-03, C Donnellan 0-02, D Hayes, I Tannian, J Coen 0-01 each.
Dublin: P Ryan 0-11 (0-06f, 0-02 '65'), M Quilty, C McCormack 0-03 each, J McCaffrey, J Boland 0-01 each.
GALWAY: F Flannery; K Hynes, D Collins, J Coen; N Donoghue, F Moore, T Óg Regan; D Burke, I Tannian; A Smith, N Burke, C Donnellan; D Hayes, J Canning, D Glennon.
Subs used: J Glynn for Smith (22 mins), J Regan for Donnellan (59), B Flaherty for Donoghue (67), C Cooney for N Burke (69).
DUBLIN: G Maguire; N Corcoran; P Kelly, P Schutte; M Carton, J Boland, S Durkin; J McCaffrey, M Quilty; C McCormack, D Treacy, L Rushe; D Sutcliffe, Ross O'Carroll, P Ryan.
Subs used: S Lambert for Treacy (45 mins), E Dillon for Quilty (57), R Treanor for Schutte (59), D Plunkett for Ryan (64).
Referee: John Sexton (Cork)
