A lucky second-half goal from Brian O'Sullivan helped Waterford edge out an improving Offaly team in the Tullamore sunshine to set up a nail-biting finale against Galway, with a place in the final possibly up for grabs.
Waterford, who lost Richie Foley to a thigh injury, led throughout but Offaly were left to rue a host of missed chances.
Deise selector Pat Bennett was more than happy to come away with the win.
"We were dreading coming to Offaly because they were buoyant after their win last week," he said.
"It was a tough, hard, physical game of hurling. We are still in with a shout."
Waterford's spread of scorers was impressive, with debutant Brian O'Sullivan shining with 1-2 from play. Foley was excellent from placed balls before going off injured with full-forward Shane Walsh the star of the show with 1-4.
The first half was for the most part a dull affair despite some excellent scoring from both sides, with Walsh particularly good.
Shane Dooley opened the scoring but a trio of points from O'Sullivan, Walsh and Foley settled the Deise.
Dooley was deadly from frees in the opening half and kept the Faithful County in touch, with Walsh firing over again in the ninth minute to give Waterford a 0-5 to 0-2 lead.
Offaly full-forward Joe Bergin came to life midway through the half and his brace of points left the scores at 0-6 to 0-5 in favour of the Deise.
Foley was in fine form from dead balls. He fired over six in the first half and had a strong part to play in the decisive score of the half.
On 32 minutes, Walsh disposed Dylan Hayden on the Offaly end line and skipped towards goal before calmly dispatching a low shot beyond the reach of Offaly custodian James Dempsey.
A late Offaly rally from Dooley and Carroll left the margin at seven points as Waterford went in leading 1-14 to 0-10 at the break.
Dooley missed a glorious goal chance early in the second half before Bergin finally found the net for the Faithful County in the 39th minute to bring it back to a five-point game.
Dooley fired over a free and a '65' but Foley was as accurate as ever for the Deise.
Waterford looked to have buried Offaly in the 57th minute when a breaking ball around the goalmouth was finished to the net by O'Sullivan, but a resilient Offaly battled back and were unlucky not to have a goal or two late on.
Dooley hit three unanswered frees and with five minutes to go Waterford only led by four points.
Walsh restored their five-point lead and, despite a late flurry from Offaly, Waterford hung on to win by three points.
Man of the Match: Shane Walsh (Waterford)
Scorers -- Waterford: R Foley 0-9 (8f, 1 '65'), S Walsh 1-4, B O'Sullivan 1-2, S Prendergast, G Crotty, S O'Sullivan, K Moran 0-1 each. Offaly: S Dooley 0-12 (10f, 1 '65'), J Bergin 1-2, B Carroll 0-3, C Egan, C Parlon 0-1 each.
Offaly -- J Dempsey 6, D Franks 6, D Kenny 6, S Egan 6; M Verney 6, R Hanniffy 7, D Morkan 7; C Mahon 8, D Hayden 6; D Molloy 6, G Healion 6, C Egan 8; S Dooley 9, J Bergin 9, B Carroll 8. Subs: M Cordial for Hayden (blood, 17-27), M Cordial 6 for Hayden (h-t), C Parlon 7 for Healion (45), J Mulrooney 6 for Molloy (50).
Waterford -- C Hennessy 6; E Murphy 6, W Hutchinson 6, N Connors 7; T Browne 9, M Walsh 8, J Nagle 7; K Moran 7, R Foley 8; S Prendergast 6, S O'Sullivan 6, S Molumphy 6; B O'Sullivan 9, S Walsh 9, G Crotty 6. Subs: P Mahoney 6 for Prendergast (53), E McGrath 6 for Molumphy (60), E Kelly 5for Foley (inj 60), D O'Sullivan 5 for Nagle (67).
Ref -- J Ryan (Tipperary).