Offaly 1-14 Waterford 0-21
Offaly had no answer to Maurice Shanahan as Waterford powered into Phase 1 of the qualifiers with victory at O'Connor Park Tullamore.
Shanahan was brilliant throughout and hit 13 points – seven of which came from play – but Michael Ryan will be infuriated with his side who hit 17 wides on a blustery evening.
But it matters little as they now go on to face Westmeath in the next round after their win over London, a challenge Waterford will be highly fancied to progress through.
It was the stronger finish that won it for the Deise men, but Offaly after trailing by four points at the break, were level 12 minutes later.
However, they ran out of steam in the last 10 minutes as Shanahan and Brian O'Sullivan cut loose.
After selecting to play against the wind after winning the toss, Offaly found themselves trailing by a couple of points early on when the lively Jake Dillon twice dissected the posts.
Nevertheless, they managed to keep in touch and seconds after Dillon slotted his second Shane Dooley pounced on a loose hand pass from Liam Lawlor in front of his own goal and gave Stephen O'Keeffe no chance from point blank range.
Ollie Baker would have been thrilled with his side's start at that stage, especially with Ger Healion and David Kenny in imperious form at the back. But Kenny's superiority was short lived as Maurice Shanahan soon began to edge the battle.
He hit frees in consecutive minutes to pull the Deise level by the 17th minute and after Dooley edged Offaly ahead in the 20th minute, Waterford hit a hot streak of four consecutive points, three of which arrived from Shanahan and two of them from play.
In the seven minutes of added time both sides hit two points each, but the last two went to Michael Ryan's men who carried a 0-13 to 1-6 lead at the break.
Playing into the stiff breeze in the second-half a four-point lead was perilous for the Deise men, and a minute after the restart they thought they had valid claim for a penalty when Seamus Prendergast looked to be dragged down by Kenny.
James McGrath didn't give it though, and instead Offaly went straight down the pitch and Brian Carroll fired a quick point.
The midfielder added another 60 seconds later to pull Offaly to within two, but they were level by the 47th minute after Brady landed his second point of the match.
But in the end Offaly looked heavy legged and with substitute Pauric Mahony impressing and Shanahan in the form of his life, Waterford eventually cruised to the win.
Waterford: S O'Keffe; S Fives, L Lawlor, N Connors; J Nagle, M Walsh, D Fives; P Prendergast (0-1), K Moran (0-1); J Dillon (0-2), S Prendergast, S O'Sullivan (0-1); J Barron, M Shanahan (0-13, 5f), B O'Sullivan (0-3).
Subs: P Mahony for Barron (35+5 mins), M O'Neill for S Prendergast (58 mins), R Foley for D Fives (63 mins).
Offaly: J Dempsey; C McDonald, D Kenny, D Mooney; R Hanniffy, G Healion, D Morkan (0-1); B Carroll (0-2), K Brady (0-2); C Egan, D Molloy, C Slevin; S Dooley (1-4, 4f), D Currams (0-2), J Bergin (0-2).
Subs: C Mahon (0-1) for Molloy (12 mins), P Cleary for Mooney (35+7 mins), S Cleary for Slevin (52 mins), S Gardner for P Cleary (56 mins), S Ryan for Brady (70 mins).
Referee: James McGrath (Westmeath).