Manager Nathan Jones picked two XIs for the contest, new addition Alfie Doughty playing the opening 45 minutes, along with former Nottingham Forest defender Baba Fernandes, currently on trial with the Hatters.
It took Town a few minutes to put their first flowing move together, ending with Elliot Thorpe beating his man on the right and forcing a decent fingertip stop from Charlie Horlock, the Hitchin keeper then comfortably collecting Henri Lansbury’s deflected long ranger.
Luton threatened again on 15 minutes, Dan Potts just unable to get on the end of Doughty's dangerous cross at the far post, as Thorpe's next attempt from Doughty's excellent run and ball in drifted tamely behind.
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Hitchin threatened sporadically, ex-Luton youngster Rio Dasilva taking advantage of a misjudgement from Fernandes, only to shoot wastefully off target.
The summer signing from Stoke, Doughty, continued to look very lively on the left flank, with some impressive control from a raking pass, only to then slice wide on his right foot.
Luton were indebted to a top stop from Harry Isted to keep the scores goalless when Josh Popoola broke the rather weak challenge of Fernandes and almost picked out the bottom corner, the keeper's fingers doing enough.
The deadlock was broken on 26 minutes though when Potts of all people took aim from 25 yards and gave Horlock little chance, firing across him and into the net.
A neat move saw Jerome feed Carlos Mendes Gomes, who managed to get it all wrong, lofting his shot over the goal, the stand and also the surrounding trees.
However, Jerome fared better with six minutes to go, bundling home at the second attempt from Thorpe's cross to double Luton's advantage.
Having made 11 changes, with summer signings Woodrow and Matt Macey getting a run-out, plus the fit-again Elijah Adebayo, the visitors should have gone further ahead in the opening 60 seconds, Onyedinma clean through only to slice tamely wide.
Town's front three of Woodrow, Adebayo and Harry Cornick only needed a few minutes to show just what a handful they could be this term too, as Adebayo sped away from his man and bent a shot against the outside of the post.
Cornick picked up the rebound, feeding Woodrow, who produced a finish of unerring quality to make it 3-0.
From there, the tempo of the play dropped quite significantly, with Luton taking until the 75th minute to look like netting again, Woodrow teeing up Bree whose measured sidefooter appeared destined for the top corner, falling inches wide.
Ex-Luton youngster Ben Stevens drilled waywardly after a mistake from Williams, before in the closing stages Hatters won a penalty when Bree was tripped inside the area.
Woodrow stepped up ahead of Adebayo, only to see another former Hatters academy graduate Tiernan Parker beat his attempt away, the rebound dropping to the forward, who just had to tap home, but somehow lofted high and wide when it was easier to score.
Adebayo might have been on target in the closing stages, as a mix-up in the Canaries defence saw the ball drop invitingly for him, but his lob from outside the box had far too much on it, drifting over the top.
He sent another header straight at Parker, while try as he might, the fit-again forward couldn’t get a late goal, being sent wide, his low drive deflected away by Parker's legs.
Hatters first half: Harry Isted, Baba Fernandes, Gabe Osho, Dan Potts, Henri Lansbury, Elliot Thorpe, Alfie Doughty, Jordan Clark, Carlos Mendes Gomes, Cameron Jerome, Admiral Muskwe.
Hatter second half: Matt Macey, Reece Burke, Tom Lockyer, Josh Williams, James Bree, Dion Pereira, Casey Pettit, Dion Pereira, Fred Onyedinma, Cauley Woodrow, Harry Cornick, Elijah Adebayo.