Richie Kehoe saw red after a 33rd minute exchange with Antrim full-forward Neil McManus but the Model men went on to dominate the third quarter despite trailing a by a point at the break.
Wexford landed five of the first six points after the restart, and when Liam Óg McGovern added his second for a seven-point cushion, Wexford looked home and hosed. Antrim then sprung back to life.
A Paul Shiels brace and a Conor Johnston point cut the gap to four. Daniel McKernan’s ground strike flew past Mark Fanning to cut the gap to the minimum on the stroke of full time, but Wexford held on for both points.
ANTRIM: C O’Connell; Ciaran Johnston, C McKinley, M Bradley; S McCrory, N McAuley, O McFadden; P Shiels (0-7, 5f), J McGreevy; D Hamill, C Carson (0-2), N McKenna (0-1); D McKernan (1-0), N McManus, C Clarke.
Subs: M Donnelly for C Clarke, S McAfee for N McManus, S McAfee for J McGreevy, Conor Johnston (0-1) for D Hamill, N McManus for M Donnelly.
WEXFORD:M Fanning; K Rossiter, M O’Hanlon, B Kenny; R Kehoe, L Chin, C Kenny; D O’Keeffe (0- 2), A Shore (0-1); S Tomkins, J Guiney (0-5, 4f, 0-1 ‘65’), I Byrne (0-1); P Morris (0-3), R Clarke, L Óg McGovern (0-2)
Subs: H Kehoe for R Clarke, G Moore for S Tomkins, R Jacob (0-1) for I Byrne, E Martin for A Shore
Referee: J McGrath (Westmeath).