A fairly strong Luton side proved too much for a young Reading side, which included Gabriel Osho, released by Reading in the summer.
Luton were the better team in the first half, with James Bree proving to be a nuisance down reading's left-hand side, as he provided a beautiful cross for Moncur, who hit it on the volley into the bottom right-hand corner.
Reading did however turn it up a gear in the second half, the best chance coming from Sone Aluko, who hit the bar from six yards out.
This result means that Luton progress to the fourth round for the first time in eight years, while Reading will now focus on getting promoted to the Premier League.
Story of the match
Both sides heavily rotated from the last time they played, with both sides making nine changes from their last Championship game.
Luton did not play last weekend due to a Covid-19 outbreak, and it did cast this game into a little doubt, but it was decided to go ahead. A notable debut for Gabriel Osho for Luton Town against the club he was released by in the summer, and the first game for Brendan Galloway since November 2019, after he recovered from a serious knee injury.
13 out of the 18 man matchday squad for Reading came through their academy, with them also making nine changes to their lineup from the 1-2 win at Huddersfield Town. A debut for Oliver Pendlebury and first starts for Jeriel Dorsett and Jayden Onen for the Royals came this afternoon.
The first chance came in the tenth minute when James Bree whipped in a cross for Ryan Tunnicliffe, who blasted his first-time volley over.
Then on the half-hour mark, Luton took a deserved lead, another cross coming in from Bree which was hoisted over to George Moncur, who calmly hit it first time into the bottom right-hand corner.
It then took Reading till after the goal to have the first few attempts on goal, the closest of which came from Pendlebury, who forced a save from Simon Sluga at his near-post.
Reading started the second half brightly but it was Luton who had the better chance at the start of the second half, Danny Hylton failing to convert from close range as Luke Southwood claimed.
The best chance of the game then fell to Sone Aluko, who hit the crossbar from six yards out after the ball fell kindly to him.
They then came close again through Tomas Esteves, who forced another save from Sluga as he shot from the edge of the box, and the Croatian goalkeeper tipped it past the post.
Reading then took aim again through Michael Olise, who tested Sluga again, forcing him again to tip the ball past the post.
The Royals then came forward again, Sam Baldock forcing a shot again testing Sluga, but Onen failed to finish follow up as Sluga saved well again.
In injury time, reading substitute Nahum Melvin-Lambert was put through on goal by Dejan Tetek, and his finish then hit the crossbar, with Onen again failing to convert from the rebound.
Man of the match - George Moncur (Luton)
The only goalscorer of the day, Moncur played very well and his goal was deserved, a calm finish which took a lot of skill to do.