Wexford will face Clare in an All-Ireland quarter-final next weekend after beating Westmeath by 2-21 to 0-16 in Mullingar.
Having lost the Joe McDonagh Cup final last weekend, the midlanders gave a decent account of themselves on their own patch tonight, but Davy Fitzgerald's charges got the job done despite failing to impress.
An Allan Devine free had the hosts within a point after 15 minutes, 0-5 to 0-4, but the winners then pulled away with five unanswered points in ten minutes, Aidan Nolan, Lee Chin (2), David Dunne and Diarmuid O'Keeffe on target.
Dunne's 26th-minute goal had the Slaneysiders seven to the good at the break, 1-12 to 0-8, and Conor McDonald's three-pointer eleven minutes after the restart settled the game as a contest (2-13 to 0-12) after Ciaran Doyle, Devine (free) and Aonghus Clarke had fired over three unanswered Westmeath points to close the gap to five.
The Lake County never looked like winning but acquitted themselves well. For Wexford, who hadn't played in four weeks, it was all about getting the job done and they will surely deliver an improved display when they meet the beaten Munster finalists.
Wexford - M Fanning; D Reck, L Ryan (0-1), S Donohoe; P Foley, M O'Hanlon, D O'Keeffe (0-1); K Foley, S Murphy (0-1); L Chin (0-7, 6f, 1'65), A Nolan (0-4), Jack O'Connor (0-1); P Morris (0-1), D Dunne (1-1), C McDonald (1-1). Subs: L Og McGovern for P Morris, W Devereux for D O'Keeffe, H Kehoe (0-2) for L Chin, S Tompkins (0-1) for Jack O'Connor, E Martin for D Reck.
Westmeath - P Carroll; C Shaw, T Doyle, J Gilligan; S Clavin, P Greville, A Clarke (0-2); E Price (0-2), D McNicholas (0-1); R Greville, C Doyle (0-1), C Boyle (0-1); N O'Brien, N Mitchell, A Devine (0-8, 7f). Subs: J Boyle (0-1) for D McNicholas, L Varley for C Boyle, D Clinton for C Doyle, A Craig for C Shaw.
Referee - D Kirwan.