A late penalty from Cameron McGeehan sees the Exiles leave Kenilworth Road empty-handed.
The Exiles named an unchanged side from Saturday's victory over Leyton Orient, with the returning Jon Parkin being named on the bench.
The host started with a menacing front line of Danny Hylton and Jack Marriott, with twenty-one-year-old Cameron McGeehan sitting just behind the front two.
Inside the opening ten munites the hosts had their first sight on goal when a bouncing effort from Jordan Cook was parried away by Joe Day and the Exiles were able to regroup to deny the hosts a chance to hit the target with a rebound.
The home side enjoyed the fair share of possession during the first half and caused a scramble inside the County area when a corner from the right bounced around the Newport area, but eventually Joss Labadie was able to clear the ball away from danger.
Five minutes before the break midfielder Mark Randall had the best chance of the half for the Exiles, when his winding run from deep allowed the creative playmaker to advance into the area, but a heavy touch at a crucial moment meant that Luton were able to clear.
Just prior to the break there was an anxious moment for Newport when a through ball was touched faintly by the sliding Scot Bennett and his deflection almost saw the ball slide past the advancing Joe Day, but the 'keeper was quick to readjust to claim the ball.
HALF TIME: LUTON TOWN 0 - 0 NEWPORT COUNTY AFC
Early in the second half Pelly Ruddock Mpanzu had a half-volley from the edge of the area that narrowly missed the left-hand post, which would have nestled into the bottom corner had the shot been on target.
Just after the hour mark, the hosts were awarded a penalty when County failed to clear a long ball forward and Jamie Turley brought down Danny Hylton inside the area. McGeehan took the penalty and slotted the ball home, after sending Joe Day the wrong way.
Luton's lead didn't last long, as eight minutes later the Exiles were level when a corner from the right by Jennison Myrie-Williams swung straight into the net, after Walton failed to grasp the ball in a crowded penalty box.
The home side were reduced to ten-men just ten minutes before the final whistle when Johnny Mullins was shown a second yellow card for a foul on Sean Rigg.
In the final minute of normal time the Exiles had a chance to strike late when Myrie-Williams played a square pass to Ben Tozer on the edge of the area and the midfielder hit a composed side-footed shot that drifted narrowly past the post.
In the fourth minute of the five added minutes of stoppage time, Pelly Ruddock Mpanzu advanced into the area and took a tumble and the referee pointed to the spot. McGeehan stepped up again to take the resulting spot-kick and the midfielder held his nerve to beat Joe Day to give Luton a dramatic late victory.
FINAL SCORE: LUTON TOWN 2 - 1 NEWPORT COUNTY AFC
Starting XI: Day, Turley, Jones, Butler, Bennett (c), Labadie, Randall (78' Tozer), Myrie-Williams, Green (66' Barnum-Bobb), Jackson (68' Parkin), Rigg
Subs: Bittner, Barnum-Bobb, Tozer, Owen-Evans, Parkin, Sheehan, Bignot
Bookings: Scot Bennett, Mark Randall, Jon Parkin, Ben Tozer, Darren Jones, Jennison Myrie-Williams
Referee: Charles Breakspear
Attendance: 7,058 (115 County fans)