Wexford accounted for Antrim on a 3-18 to 0-17 scoreline to end the Saffrons' All-Ireland SHC involvement at Wexford Park.
Liam Dunne's men laid the foundations for this win in the opening half with Podge Doran and Rory Jacob claiming goals.
But Antrim were only 2-05 to 0-09 in arrears at the break thanks to some superb scores from free-taker Neil McManus.
The visitors remained competitive until Paul Morris' 56th-minute goal confirmed Wexford's date with Carlow next Saturday.
Wexford's best moment came when they crafted a superb third goal to decide a game that was played in blustery conditions, with Antrim well in the hunt up to that point.
Rory Jacob gained possession and slipped a lovely pass through to Morris who struck a sweet left-handed shot to the back of the Antrim net.
That goal put Wexford six points up and they ran out convincing winners with some fine long range points from captain Garrett Sinnott, Éanna Martin and Shaun Murphy to give them a somewhat flattering 10-point winning margin.
Antrim, with a wind advantage, were sharp early on and led by 0-05 to 0-03 after fifteen mintutes. The Antrim scores included a couple of outstanding long range efforts from centre-back McManus - one of them a 70-metre free.
Antrim were rocked however midway through the half when Wexford corner forward Doran scored the opening goal of the game from close range, scrambling home from a few metres out after goalkeeper Chris O'Connell had denied Morris.
Undeterred, Antrim replied and coming up towards the interval they had forged their way back in front by a point. They could have had a goal on the scoreboard but a kicked effort from Karl Stewart went narrowly wide.
On the stroke of half-time however, Wexford's hopes received a huge boost when Jacob netted. The alert attacker pulled first time on the ball to send a low ground shot to the net after Sinnott's point attempt effort had come back off the post.
Despite playing against the strong wind in the second period, the Glensmen made good use of possession and with Simon McCrory also in fine form in defence they kept in touch.
But Morris' neatly finised goal sealed the home side's place in the next round of the qualifiers, with impressive wing forward Jack Guiney top-scoring in the end with 0-08 (including six placed balls).
Wexford's prize is a Leinster derby against Carlow at Wexford Park next Saturday, while Antrim's Championship hopes ended today but not without a game battle.
WEXFORD: M Fanning; E Moore, T Waters, B Kenny; R Kehoe, M O'Regan, C Kenny; D Redmond, L Chin; J Guiney (0-08, 0-03f, 0-02 '65', 0-01sl), G Sinnott (0-04), H Kehoe; P Morris (1-02), P Doran (1-00), R Jacob (1-02).
Subs used: C O'Shaugnessy for Doran (48 mins), E Quigley for Redmond (59), J Tonks for H Kehoe (60), S Murphy (0-01) for Kenny (66), E Martin (0-01, 0-01f) for Chin (68).
ANTRIM: C O’Connell; B McFall, A Graffin, C McKinley; S McCrory, N McManus (0-06, 0-02f), P Shiels; J McGreevey (0-02), N McAuley; S McNaughton (0-05, 0-03f), C Carson (0-01), T McCloskey; C McGuinness (0-01), K Stewart (0-02, 0-01f), D Hamill.
Subs used: O McFadden for McFall (43 mins), C Clarke for McGuinness, K McKernan for Carson (both 60).
Referee: John Sexton (Cork)
Highlights and analysis of all the weekend’s action on The Sunday Game from 22:00 on Sunday 23 June on RTÉ Two and RTÉ.ie (Ireland only).
Expert and fan reaction on Take Your Point from 18:00 on Sunday 23 June on RTÉ Radio 1 and RTÉ.ie (Worldwide).