Story of the match
Luton boss Nathan Jones made eight changes to the side that defeated Swansea City in the Championship with Jed Steer making his debut on loan from Aston Villa and Elliot Thorpe named to the starting XI for the first time in his senior career.
Luton were in front in the 13th minute as Thorpe picked out Burke, who headed past U's goalkeeper Dimitar Mitov into the far corner.
Nine minutes later, the lead was doubled. Jerome picked out Gomes on the edge of the box and the Brazilian fired low past Mitov to put the Championship outfit in commanding position.
Soon after the restart, Tom Lockyer got on the end of a knockdown by Muskwe, but he steered it over the bar from close range.
In the closing moments, Hoolahan and Brophy saw shots blocked and Steer saved from Ben Worman.
Two minutes from time, Muskwe collected a pass from substitute Harry Cornick and his left-footed drive was deflected by Sam Sherring and past a helpless Mitov.
Man of the match: Cameron Jerome
A veteran that has played in the Premier League before, he was especially dangerous in the early stages of the game, just missing with his attempt going on to set up Luton's opener.