But Wexford boss Larry Coleman had some cause for concern when his side led by just four points at the interval having played with a gale-force wind.
Eoghan Cahill’s pointed free had Offaly in front inside three minutes but Wexford, despite their outfield dominance, had to be content with a succession of points from Joe Coleman (four), Cathal Dunbar, Sean Kelly, Darragh Pepper, Matthew Joyce, Daire Barden and Joe O’Connor to lead 0-9 to 0-1 after 25 minutes.
Cahill and Coleman, free, exchanged points, before sub Conor Freeman shot a goal just on half-time followed by a Cillian Kiely pointed free to leave the homeside leading 0-10 to 1-3 at the interval.
Wexford increased their lead with four early second half points, and while Cillian Kiely pointed frees kept Offaly in touch, the home side who finished with three points through sub Kevin Poole, Coleman and Pepper.
Scorers for Wexford: J Coleman (0-7fs), D Pepper (0-3), D Barden (0-2), C Dunbar, S Kelly, M Joyce, J Firman, J O’Connor, K Poole (0-1 each).
Scorers for Offaly: C Freeman (1-1), C Kiely (0-4, 2fs, 1 65), E Cahill (0-3, 1f), O Kelly (0-1).
WEXFORD: D Hughes; B Edwards, M O’Brien, R White; N Rossiter, A Maddock, C Firman; C Dunbar, N Hughes; S Kelly, D Barden, M Joyce; J Firman, J Coleman, D Pepper.
Subs: J O’Connor for Edwards; K Poole for Kelly; S Casey for Joyce; R Donohoe for Dunbar.
OFFALY: O Mahon; P Delaney, C Taylor, N Duffy; C Molloy, D Spain, D Mahon; C Kiely, P Guinan; C Cleary, O Kelly, R Hughes; J Fogarty, J Kilmartin, E Cahill.
Subs: C Freeman for Cleary; D Buckley for Guinan (52), E Carroll for Spain (52), D Wyer for Hughes.
Referee: R Byrne (Kilkenny).