A GOAL from full-forward Tom Walsh proved the decisive score at Pairc Tailteann as Meath advanced to a clash with Louth.
Walsh struck the Royals' only score from play in the second half after 50 minutes to put his side six points ahead, 1-11 to 1-5.
The Walterstown clubman clocked up an impressive 1-3, while Graham Reilly knocked over five points, four from frees.
Despite the defeat, Wexford manager Jason Ryan will have found positives in his team's performance as they recovered from a poor start to play some attractive football.
The second-half introductions of Rory Quinlivan, Padraig Kelly and Adrian Flynn added fluidity, with Ben Brosnan and Graeme Molloy also showing well.
A whirlwind start from the hosts brought seven points within 13 minutes.
Walsh accounted for three of those scores and Reilly two, in a spell of complete Meath dominance.
Wexford eventually came to life after captain PJ Banville netted from close range following slack defensive play from the home side on 20 minutes.
Brosnan added a quick point and the Meath goal was charmed when Banville saw his cracking shot rebound off the crossbar.
Further points from Banville (free) and wing-back Lee Chin reduced the deficit to the minimum by 28 minutes.
However Meath finished the half stronger and points from Reilly, Conor Gillespie, newcomer Alan Forde and Paddy Gilsenan left it 0-11 to 1-3 at the break.
Points from Eric Bradley and Kevin O'Grady reduced the deficit at the start of the second half but the concession of that goal was conclusive.
SCORERS -- Meath: T Walsh 1-3 (0-1 '45'), G Reilly 0-5 (4f), P Gilsenan 0-2, M Burke, C Gillespie, A Forde 0-1 each. Wexford: PJ Banville 1-0, B Brosnan 0-3 (1f), A Flynn 0-2, L Chin, E Bradley, K O'Grady (f), R Quinlivan, P Kelly 0-1 each.
MEATH -- D Gallagher; G O'Brien, B Menton, M Burke; C McGuinness, S McAnarney, C Lenehan; M Ward, C Gillespie; B Meade, G Reilly, D Tobin; P Gilsenan, T Walsh, A Forde. Subs: C O'Connor for Lenehan (28 mins), D Smyth for Forde (48), B Hanlon for Meade (60), J Carry Lynch for Gillespie (67), C O'Dwyer for Reilly (69).
WEXFORD -- T Hughes; N Murphy, F Lancaster, S Culleton; L Chin, G Molloy, B Malone; D Waters, A Shore; E Bradley, B Brosnan, PJ Banville; P Byrne, K O'Grady, K Rowe. Subs: A Flynn for Chin (51), P Kelly for O'Grady (51), R Quinlivan for Shore (55), S Banville for Rowe (63), A Doyle for Bradley (68).
REF -- P Kneel (Louth)