Barton took the lead in the 12th minute through Mark Kenneford, before Keshi Andersen added the second and third to make it 3-0 by the break.
Rovers continued to dominate in the second half and Kenneford notched his second on 52 minutes, while Nat Peacock swiftly added a fifth.
Andersen set up Rhys Hoenes to head home, before Peacock doubled his tally and then turned provider for Bilal Hassan to score the eighth.
Peacock rounded off his hat-trick late on as boss Dan Kennoy said: “It was a great confidence boost for the squad.
Jones could loan out Muskwe and Mendes Gomes as he admits certain players would have left regardless of cup exit
Jones still keen on pushing for defensive signing ahead of deadline day
Former Aston Villa and Crystal Palace youngster Williams elated to make his full Hatters debut in Carabao Cup
Luton boss will make a late decision in the transfer window on whether to loan out Pereira
Jones hopeful that Onyedinma is soon over his 'unfortunate year' for Luton
“It’s important we keep our feet on the floor and continue the hard work as we go into a run of games now that will test us.”
Rovers face Arlesey tonight, Harlow on Saturday and then St Albans next Tuesday.