A strong first half showing set up Galway for a 0-15 to 0-12 victory at a bitterly cold Walsh Park.
Joe Canning, who had a 14th minute penalty saved, contributed three points and there were braces from Iarla Tannian and Niall Burke as the Tribesmen led 0-08 to 0-03 at half-time.
Waterford's Maurice Shanahan and Seamus Prendergast cut the gap to three points, but the lively Davy Glennon and Canning sealed a result that puts Galway through to the semi-finals.
This was an untidy contest, but Galway's effective first-half performance laid the foundations as they held a healthy five-point lead by the interval despite playing into a howling wind.
Tannian and Glennon came up trumps for the Tribesmen and a robust defensive unit also restricted the home side.
Galway laid down a marker early on as they outmuscled and outfought their opponents. Canning saw his penalty saved on 14 minutes, however Anthony Cunningham's determined side dictated matters.
Tannian led the charge with a dominant display at midfield as he struck two first-half points.
Waterford hung onto the coat-tails of the visitors early on and the sides traded two apiece.
Niall Burke and Canning made it 0-04 to 0-02 to Galway before Brian O'Halloran pegged one back on 13 minutes. That would prove to be Waterford's last score of the half, however, as the Tribesmen shut down the space.
Galway hit four points without reply with Tannian, Canning (0-02) and Niall Burke all on the mark.
Waterford battled back in the second half and reduced the deficit to three points. Seamus Prendergast was causing problems at the edge of the square and Maurice Shanahan scored three points to leave it 0-10 to 0-07 on 48 minutes.
David Burke replied for Galway and then Colm Callanan saved Shanahan's close-in free.
The Tribesmen pushed on from there as Glennon racked up his fourth point from play and Cyril Donnellan also contributed as they opened up a six-point advantage.
Shanahan continued to keep the scoreboard ticking over for Waterford, but two points from Canning kept Galway in command (0-15 to 0-10) with five minutes left.
The hosts continued to press for the precious point that would have ensured their place in the knockout stages.
Shane O'Sullivan split the posts and then Shanahan sent over his seventh point of the afternoon to leave only a single score between the sides. However, Cunningham's men survived and they will renew rivalries with Kilkenny in the last-four.
WATERFORD: I O'Regan; S Fives, L Lawlor, S Daniels; J Nagle, M Walsh, D Fives; S O'Sullivan (0-01), K Moran; R Barry, S Prendergast (0-01), B O'Halloran (0-01); J Dillon (0-01, 0-01f), M Shanahan (0-07, 0-05f, 0-01 '65'), J Barron (0-01).
Subs used: P Mahony for O'Halloran (53 mins), S Walsh for Barry (59), B O’Sullivan for Dillon (63).
GALWAY: C Callanan; F Moore, K Hynes, N Donoghue; A Harte, D Collins, J Coen; I Tannian (0-02), J Cooney; D Burke (0-01), C Cooney, J Canning (0-05, 0-03f); D Glennon (0-04), C Donnellan (0-01), N Burke (0-02).
Subs used: D Hayes for N Burke (53 mins), A Smyth for J Cooney (57), J Glynn for C Cooney (61), J Regan for Donnellan (68), B Flaherty for D Burke (70).
Referee: Anthony Stapleton (Laois)