Offaly 0-15 Waterford 0-10
Niall McNamee fired five points as Offaly claimed back-to-back All-Ireland SFC qualifier victories for the first time since 2003.
McNamee scored early on in Tullamore as Offaly edged ahead of Waterford, and they were 0-9 to 0-6 to the good at half-time. Conor McGrath and Gary Hurney had kept the Deise in touch.
The Faithfuls pressed on and despite hitting a number of wides, including a Paul McConway goal miss, late points from Anton Sullivan and McNamee sealed the home win.
Offaly manager Tom Cribbin was forced to use five different free-takers in this match, before eventually settling on McNamee who slotted over two second-half points from placed balls.
It was Offaly who had the early breaks in the midfield sector but they failed to convert their early scoring chances, and it was Waterford who hit the front through McGrath in the sixth minute.
However, this was the only time that John Owens' charges led during a hard-fought opening half. Pre-match favourites Offaly strode ahea dby kicking four unanswered points between the ninth and 17th minutes.
Graham Guilfoyle got the hosts off the mark. Team captain Karol Slattery made a lung-bursting run from 45 metres out, before laying off the ball to Guilfoyle who slotted over from close range.
A brace of scores from Niall McNamee pushed Offaly 0-3 to 0-1 ahead in the 15th minute, and the scoring chances were coming quick and fast for Cribbin's men.
With a goal on the cards in the 16th minute, Brian Connor was denied by a superb save from Waterford stopper Tom Wall, but Ciaran McManus pushed his side three points clear from the resulting '45'.
Guilfoyle had a good opportunity to extend the home side's lead to four soon after, but Waterford full-back Tomas O'Gorman stood firm.
The Deise suddenly found their stride in attack, knocking over four of the next six points through Patrick Hurney, McGrath, Gary Hurney and Shane Briggs.
Slattery was forced off with a hamstring injury, in a significant blow for Offaly, but the Faithfuls recovered well to tag on points from McNamee, Scott Brady and Ken Casey before half-time.
Offaly started the second half in strong fashion, winning the opening exchanges at midfield, with scores from McManus and Guilfoyle extending their advantage to five points - 0-11 to 0-6.
Gary Hurney pegged a point back for the visitors, with two goal-scoring opportunities arriving for his side in a two-minute spell.
A 47th minute effort off the ground from Patrick Hurney finished in the hands of Offaly goalkeeper Alan Mulhall, before a McGrath shot was blocked out by McManus, and Michael Donnelly failed to convert the resulting '45'.
Gary Hurney cut the gap to three by registering his third point of the contest as the game entered the final quarter, but Offaly had the better of the closing stages to book their place in tomorrow evening's third round draw.
Scorers: Offaly: N McNamee 0-5 (0-2f), C McManus 0-3 (0-1 '45', 0-1f), G Guilfoyle, A Sullivan 0-2 each, K Casey, B Connor, R Brady (0-1f) 0-1 each
Waterford: G Hurney 0-5 (0-3f), C McGrath 0-2, S Briggs, M Donnelly, P Hurney 0-1 each.
OFFALY: A Mulhall; B Darby, S Brady, S Pender; K Slattery, R Brady, N Darby; R Dalton, J Coughlan; G Guilfoyle, B Connor, C McManus; K Casey, A Sullivan, N McNamee.
Subs used: P McConway for Slattery (26 mins), J Reynolds for Guilfoyle (55), S Ryan for Coughlan (59), A McNamee for Casey (67).
WATERFORD: T Wall; M O’Gorman, T O’Gorman, K Connery; N Hennessy, S Briggs (0-1), K Phelan; M Aherne, K Power; W Hennessy, C McGrath, M Donnelly; B Wall, G Hurney, P Hurney.
Subs used: C Phelan for Connery (34 mins), L O'Lionain for W Hennessy (44), S Cunningham for P Hurney (55), J Hurney for N Hennessy (59), C O'Keefe for McGrath (67).
Referee: Aidan Mangan (Kerry)