It takes them into the Division One semi-finals for the first time in the county's history.
The teams were level five times at Wexford Park in a superb game that ebbed and flowed more than the nearby River Slaney; a tussle which the home side desperately needed to win to ensure that an excellent spring campaign did not again dissipate into ultimate disappointment.
This was the fifth time in five years Wexford had found themselves sniffing a semi-final spot on the last day of the league, yet only once previously had they managed to seal the deal.
Last week's defeat to Galway at this same venue left them peering anxiously over their shoulders yet again, but three points inside the last 10 minutes from Darragh Breen, Paddy Colfer and Matty Forde finally took them clear of Laois and booked an appointment with Tyrone in two weeks at HQ.
"For everyone involved in Wexford football, we were determined we wouldn't (fall short) again today," said Forde afterwards.
"We got caught on the hop a little last week, maybe we got caught up in the hype but we concentrated on the task in hand today and came out on the right side of a very tight game."
Manager Pat Roe has long said this team has only reached the base-camp of its ambition and potential, but the psychological effects of losing out on the last four would have been too grim to bear, as the Laois native said afterwards.
"Last weekend was the first weekend we were out of the top spot and to lose today would have been very difficult. We said before the game that this was a test of how far we had moved from last year. We fell at the last hurdle last year but we've gone an extra stride this time.
"We're in a difficult position in that we've never been here before, the other three have. It is a big step for us but the semi-finals will be another test for us to gauge ourselves against the very best."
The main worry for Roe ahead of Tyrone and the championship will be his midfield, which was destroyed by an oft-criticised Laois centre pairing of Noel Garvan and Padraic Clancy yesterday. Elsewhere though, the signs are invariably promising.
Forde may have again finished top scorer on the day with a tally of 1-5 but four of his points came from dead balls. Clearly, his supporting crew up front are chipping in far more than was the case last year.
The foundation stone for this team though, is their full-back line of Colm Morris, Philip Wallace and Niall Murphy, a trio who have played every league game bar one as a unit since early February.
Only once did Laois come close to penetrating that line for a goal, Ross Munnelly's shot being smothered by goalkeeper John Cooper four minutes in. Laois have managed only two goals in the league, a paltry return compared to Wexford's 12.
Two of those arrived yesterday and both were crucial. The first came 13 minutes in with Laois 0-4 to 0-1 in front and dominating all over the park.
Paul Begley misjudged the bounce of a long ball in from Diarmuid Kinsella and that allowed Forde all the time in the world to strike low into the net.
The second arrived on the threshold of half-time, when Breen provided the icing on a move initiated by Colfer and carried on by Diarmuid Kinsella.
That left it 2-7 to 0-9 in the home side's favour.
Laois, with neither a play-off or relegation to bother them, bounced back with four successive scores inside six minutes on the restart, yet their momentum was cruelly checked by a ridiculous yellow card for midfielder Padraig Clancy just when he was grabbing the game by the throat.
"Clancy getting sent off was a big loss for us because he was going great guns for us," said Mick O'Dwyer.
"We had really got on top at that stage, but we're quite happy with how we played. Winning or losing made no great difference for us," he said.
Maybe so, but the irony of it is that Laois seem to need another competitive fixture far more than Wexford. All spring O'Dwyer has mixed and matched his resources like an alchemist looking to turn base metals into gold, but his work is far from done.
Munnelly is back to the form he showed in 2003 while Donie Brennan will certainly play a prominent part in their Leinster campaign, but questions still remain over many positions.
Of all the new faces called on to audition for defensive roles, only U21 Padraig McMahon looks to have nailed down a starting place for their provincial quarter-final at the end of May. Naming their starting line-up for their opening championship outing will be far from an easy task.
: J Cooper; C Morris, P Wallace, N Murphy; R Mageean, D Murphy, S Cullen; D Kinsella (0-1), N Lambert; R Barry (0-1), P Colfer (0-2), J Hegarty (0-1); D Fogarty (0-1), J Hudson, M Forde (1-5, 4f). Subs: K Kennedy for Fogarty 17, B Doyle for Lambert 24, D Breen (1-1) for N Murphy 26, PJ Banville for Kennedy 61, G Sunderland for Morris 70.
: F Byron; D Conroy, D Rooney, P Begley; A Fennelly, P McMahon, P McDonald; P Clancy, N Garvan (0-1); R Munnelly (0-3, 2f), C Conway (0-3f), D Miller (0-2); S Cooke (0-3), S Kelly (0-1), B Sheehan.
: J Higgins for Conroy 22, C Begley (0-1) for P Begley 35, D Brennan (0-1) for Kelly 35, M Dunne for Clancy 45 (YC), I Fitzgerald for Sheehan 57, P Lawlor for Miller 67, Conway (YC) 69.
: S McCormack (Meath).