Brothers Noel and Stephen Hunt set the home side on their way, setting each other up for a goal each inside the first 15 minutes, before academy stars Alex Pearce and Jem Karacan made victory certain with their first senior goals for the club.
Steve Coppell's young side took control of the tie from the first whistle and effectively killed the game off inside a quarter of an hour.
Noel Hunt opened the scoring with a clinical header on 11 minutes, racing in ahead of a static defence to power home from his brother's pinpoint corner.
Four minutes later, Hunt the younger returned the favour, curling a clever pass beyond Claude Gnakpa that invited Stephen to run on to and turn neatly home.
From then on it was just a case of how many for Reading's young side.
Pearce narrowly failed to connect in front of an open goal after Ivar Ingimarsson had flicked on James Henry's free-kick and Shane Long then forced Luton keeper Conrad Logan to block with his legs.
It was Logan's first start for the Hatters after joining on loan from Leicester and it was a baptism of fire for the keeper, who was offered little protection.
Teenage defender Pearce headed a third from Henry's corner nine minutes into the second half and a minute later it was four as Henry sent Long racing clear down the right and the Irishman set up Karacan for a far-post tap-in.
Henry, the creator of so much of Reading's best openings, then claimed the goal he deserved as Noel Hunt capitalised on some shambolic defending to run in and tee the winger up for a debut goal, before Luton sub Ryan Charles bundled one back 10 minutes from time.