The visitors produced a storming first half and led by 2-10 to 0-7 having played against a very strong wind, with Stephen Quirke scoring both Offaly goals.
Offaly’s Shane Dooley was sent off in the 50th minute and Westmeath then gained a foothold with Brendan Murtagh firing home a goal.
In the closing stages Westmeath had a goal controversially disallowed but Offaly ran out winners with late points from Emmett Nolan and Tom Carroll.
Scorers for Offaly: S. Quirke 2-0, S. Dooley 0-5 (0-4 frees), E. Nolan 0-4 (0-3 frees), T. Carroll 0-3, S. Ryan 0-1, S. Kinsella 0-1, P. Murphy 0-1.
Scorers for Westmeath: B. Murtagh 1-7 (0-6 frees, 0-1 from a 65), N. Dowdall 0-2, E. Corrigan 0-2, C. Boyle 0-1, A. Devine 0-1.
OFFALY: J. Dempsey; P. Camon, D. Shortt, S. Egan; E. Nolan, C. Egan, C. Parlon; S. Wynne, S. Ryan; T. Carroll, S. Kinsella, G. Mann; S. Dooley, P. Murphy, S. Quirke.
Subs: C. Kiely for G. Mann (54 minutes), B. Carroll for S. Kinsella (61), D. Currams for S. Quirke (64), D. Mooney for C. Parlon (68).
WESTMEATH: A. Doyle; C. Shaw, A. Craig, K. Duncan; A. McGrath, T. Gallagher, L. Varley; K. Murphy, S. Power; N. Dowdall, B. Murtagh, N. Mitchell; E. Price, A. Price, D. Clinton.
Subs: S. McGovern for A. Doyle (injured, 6), A. Devine for S. Power (27), C. Boyle for A. Price (half time), E. Corrigan for D. Clinton (54), J. Boyle for E. Price (69).
Referee: Gavin Quilty (Kilkenny).