It had not looked like the Hatters would make such easy work of it early on, with the Robins coming closest in the first half as they dominated possession.
Derrick Williams rifled over the top and Callum Robinson nodded narrowly wide, while Korey Smith shot straight at goalkeeper Mark Tyler, who then brilliantly tipped over Robinson’s attempt.
Luton started to get a foothold, though, and took the lead in the 43rd minute when Marriott turned his man inside and out before finding the bottom corner via the post.
Luton doubled their advantage after 59 minutes when Pelly Ruddock Mpanzu’s through ball was inch perfect for Paul Benson to take in his stride and beat Ben Hamer.
Tyler made a superb stop from forward Jonathan Kodjia’s daisy-cutter before the hosts enjoyed some breathing space as Marriott pounced for his second of the night in the 63rd minute, collecting the loose ball from a defensive error and drilling low into the net.
Robinson pulled one back with 19 minutes to go as Town switched off at the back, but once sub Kieran Agard put a free header wide, there was no way back.