Captain Sam Mulroy fired 2-04 as Louth turned on the afterburners in the final quarter in Portlaoise, easing beyond Wexford to secure a Leinster SFC semi-final clash with Kildare.
Just three points separated the teams approaching the hour mark after an entertaining contest but two Mulroy goals in the closing quarter, both from penalty kicks, propelled Ger Brennan's side to victory.
The seven-point winning margin flattered them slightly though National League status ultimately told as Louth, who operated two divisions higher than Wexford, brought their big game experience to bear.
Ciaran Downey scored Louth's other two goals while Ciaran Keenan won both penalties and there were important scores too from Liam Jackson and Ryan Burns as Louth turned the screw late on.
Last season's Leinster finalists will return to Croke Park in a fortnight to face the Lilywhites though Wexford will return to the Tailteann Cup next month.
John Hegarty's side, who gave themselves a fighting chance with a strong midfield display, will rue the goal concessions and the sloppy fouls for the penalties in particular.
Wexford were chasing a first quarter-final win since beating Longford a decade ago and they led for the majority of the first-half after a bright opening.
Ben Brosnan was a late addition to their published lineup, making his 177th appearance for the county, though it was his colleague in the inside forward line Graeme Cullen that impressed initially.
Cullen fired three points as Wexford opened up a 0-08 to 0-04 lead after 27 minutes, defying the wind and outbreaks of rain with some impressive bursts up the pitch.
One of those came in the 14th minute and resulted in a Cullen point though Louth fans were aghast as they argued that Ryan Burns had been fouled by Tom Moran at the other end and that a penalty should have been awarded.
Wexford capitalised on that occasion with the lightning fast counter-attack while they profited generally from Mark Rossiter's influence in attack.
The wing-forward nailed one point and hit the crossbar on another occasion, resulting in an eventual score for Cullen.
Louth, who held their own again this season in Division 2, were surprisingly clinging on against the Division 4 outfit but suddenly burst into life late in the half with an unanswered 1-02.
Tommy Durnin pinched a point before Downey eventually tied it up at 1-05 to 0-08, slamming to the net for Louth after a series of quick hand-passes across the 20-metre line found him free on the left.
Tom Jackson capped off the scoring surge with a Louth point to nudge them ahead for the first-time, 1-06 to 0-08, and it remained that way at the break.
Wexford's Glen Malone tied it up shortly after the restart before a goalmouth scramble at the other end in the 40th minute. Burns and Sam Mulroy both had shots blocked, firstly by the goalkeeper and then by defender Darragh Lyons. Wexford got away with that one though corner-back Eoin Porter was shown a black card when the dust settled.
Wexford coped with the loss well, winning that 10-minute period by 0-01 to 0-00, Sean Nolan with the score to edge them back in front.
The final 20 minutes was all about Louth though as they pushed on for the anticipated win with captain Mulroy taking on the responsibility twice from the penalty spot in the 59th and 67th minutes.
Louth: Niall McDonnell; Donal McKenny, Dermot Campbell, Peter Lynch; Leonard Grey, Anthony Williams, Conall McKeever; Tommy Durnin (0-02), Ciaran Murphy; Ciaran Downey (2-00), Ciaran Keenan, Conor Grimes (0-01, 0-01m); Ryan Burns (0-01), Sam Mulroy (2-04, 1-00 pen, 0-04f), Tom Jackson (0-01).
Subs: Liam Jackson (0-01) for Tom Jackson 46, Niall Sharkey for Grey 46, Bevan Duffy for Murphy 46, Dan Corcoran for Campbell 63, Paul Matthews for Durnin 68.
Wexford: Rory Tubritt; Gavin Sheehan, Darragh Lyons, Eoin Porter; Dylan Furlong, Paraic Hughes (0-02), Glen Malone (0-02); Liam Coleman (0-02, 0-01 45), Niall Hughes; Kevin O'Grady (0-01), Eoghan Nolan, Mark Rossiter (0-02); Graeme Cullen (0-03), Sean Nolan (0-03, 0-02f), Ben Brosnan.
Subs: Tom Byrne for Eoghan Nolan 49, Conor Kinsella for Brosnan 49, Richie Waters for Cullen 61, Shane Pettit for Rossiter 66, Jonathan Bealin for O'Grady 70.
Referee: Seamus Mulhare (Laois).
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