A Michael Meehan goal six minutes from time rescued Galway from one of the shocks of the summer as they finally edged out Waterford at Pearse Stadium.
Galway led by 0-10 to -7 having played with the wind but Waterford scored six points without reply after the restart to surge 0-13 to 0--7 in front with 15 minutes left.
They still led by a point when Sean Armstrong set up Meehan for the only goal of the game to deny Waterford a famous win.
Waterford kept plenty of players behind the ball in the opening half when they were playing against the wind and Galway struggled to break them down.
Galway had started promisingly with three points from Meehan in the opening six minutes, but they struggled to build on that promising start and only led by a goal at the interval.
Waterford seized control after the restart and with man of the match Paul Whyte in superb form — he scored 0-08 in a magnificent display — they quickly reduced the deficit.
Four of his points from play and he leveled the sides after 46 minutes with his fourth effort.
Whyte added two more in addition to one from captain Gary Hurney and Galway looked to be in serious trouble.
They went 23 minutes of the second-half before they got their first score, a pointed free from Armstrong and then after Michael Martin reduced the margin to a point, Armstrong set Meehan up for the crucial score of the game and the Galway full-forward blasted to the net.
Whyte landed a 45 to leave the minimum between them but Galway held on for victory in the end to book their place in the third round in two weeks.
Galway: M Breathnach; C Forde, F Hanley, J Duane; C Doherty, G O’Donnell, G Sice; P Conroy (0-04, 0-02f), G Higgins; J O’Brien; S Armstrong (0-01f), M Farragher; D Cummins (0-01), M Meehan (1-5, 0-01f, 0-01 ’45), M Hehir.
Subs: K Kelly for Forde (28 mins), M Martin for Hehir (45 mins), T Flynn for Higgins (49 mins), S Denvir for Doherty (52 mins), F O Curraion for O’Brien (60 mins).
Waterford: S Enright; N Walsh, T O’Gorman, M O’Gorman; C O’Keeffe, S Briggs, C Phelan; T Prendergast, S Ahearne; T Grey (0-1), G Hurney (0-02), A Doyle (0-02); B Wall, P Whyte (0-08 0-03f, 0-01 ’45), L O Lionáin.
Subs: R Ahearne (0-01) for Wall (60 mins), D Allen for Prendergast (68 mins).
Referee: D Fahy (Longford).
Highlights and analysis of all the weekend’s action on The Sunday Game from 21:30 on Sunday 6 July on RTÉ Two and RTÉ.ie (Ireland only). Expert and fan reaction on Take Your Point from 18:00 on RTÉ Radio 1 and RTÉ.ie (Worldwide).