A goal in each half from Scott Rendell booked the Town a second round FA Cup tie at home to Dorchester.
The striker fired the Hatters ahead midway through a first half dominated by Paul Buckle's side when converting JJ O'Donnell's cross.
Nuneaton pressed after the break but they failed to call Mark Tyler into any action and the Hatters punished the hosts when Rendell notched his second 17 minutes from the end from the penalty spot after Andre Gray was fouled in the box and that's the way it stayed.
It all began with Buckle making four changes to the side that disappointed against Dartford with Mark Tyler replacing Dean Brill in goal. A leg injury to Stuart Fleetwood meant he missed out which meant a start for Dan Walker. With Jonathan Smith and Simon Ainge unavailable to play, there were starts for Lathaniel Rowe-Turner and Janos Kovacs.
It was Kovacs that almost put the Town ahead inside three minutes. The Hungarian met Alex Lawless' dangerous corner from the right to nod towards the top corner but his goal-bound effort was headed off the line by Adam Walker.
A minute later Tyler comfortably gathered Gavin Cowan's header before the Town came close again. Enjoying space down the left flank, JJ O'Donnell beat his man to send a low cross into the feet of Rendell. His lay-off found Gray but his firm shot was blocked by a home defender.
In truth the first 15 minutes was pretty low-key stuff; Town threatened with the pace of Gray and Walker whilst Nuneaton were waiting patiently for their chance on the counter attack.
But the most eye-catching aspect of the Hatters' play was the wing play and O'Donnell's persistence and skill led to the opener on 22 minutes. He skipped past Kevin Malaga down the left to dart to the bye-line and his low cross was turned in emphatically by Rendell from six yards.
Nuneaton's forays forward were few and far between but just before the half-hour mark they won their first corner from which James Armson hammered a shot that whistled through sea of bodies in the penalty and behind for a goal-kick.
Seven minutes before the break it was almost 2-0 to the Town when a fine defence-splitting pass from Kovacs sent Walker scampering down the right. His high cross to the back post was headed down by Gray to Rendell but the Town goalscorer could not turn the ball home inside the six yard box.
However, two minutes later Boro were almost level. Kovacs' foul on Brown looked harsh but from the resultant free-kick Brown glanced a header onto the foot of the post with Tyler beaten. Tyrell Waite, the Boro scorer in the first game, then blazed way over from the rebound.
The Town then had a chance from a set-piece themselves a minute before the break when Lawless' free-kick was headed goalwards by Rendell, but home goalkeeper Ben McNamara was able to make a comfortable catch.
Neither side made any changes at the break but Nuneaton should have levelled 60 seconds after the restart when Tom James sped clear of the Town defence down the left but his firm shot was well-saved by the legs of Tyler.
A minute later Waite sent a fierce drive from the edge of the area flashing wide as Boro looked dangerous in search of an equaliser early in the second half.
Back came the Town, Gray firing a shot out of nothing a yard or so wide on 54 minutes before Walker made way for Matt Robinson in Buckle's first change.
Boro came agonisingly close to equalising just before the hour, Kovacs snuffing out the danger at the near post before Brown headed the resultant corner inches wide of the post.
While Nuneaton pushed men forward the Hatters had plenty of space to exploit on the break and Gray helped an off-target shot from Robinson over the crossbar following another positive break down the left by O'Donnell.
Nuneaton wasted a free-kick when James blazed over from the edge of the box before a fine intervention from Howells prevented a left-wing cross falling for Brown in the six-yard box.
However, Boro's profligacy in front of goal was punished by the Town on 72 minutes when Rendell got his second of the night. Gray chased a long ball down-field into the penalty area and was wrestled to the floor by home captain Gaz Dean and referee Ward pointed to the spot. Up stepped the ever-cool Rendell to send the keeper the wrong way for his ninth goal of the season.
Rendell almost got a third two minutes later when he took a fine pass from Robinson to bear down on goal but, after a delicate touch, home stopper McNamara was able to thwart the Town's two-goal hero.
Nuneaton's threat had diminished following the second goal and the Hatters had the luxury of making two late changes with Jake Woolley and James Dance making late appearances in injury time. For Dance it was his first appearance in Luton colours since 18th January.
And, after four additional minutes added the Town held on comfortably to record their eighth away win of the season and with it the prize of a second round tie against a Dorchester team they will also face in the FA Trophy.