Luke Guttridge put the hosts in front with a marvellous long-range strike, before Jan Klukowski levelled the tie after half time.
Paul Benson then nodded Luton back into the lead, but Newport levelled once more as former Hatter Aaron O’Connor headed home.
However, Luton went on to triumph thanks to Ricky Miller’s first goal for the club and Jake Howells’ fine solo effort.
Former Aston Villa and Crystal Palace youngster Williams elated to make his full Hatters debut in Carabao Cup
Jones could loan out Muskwe and Mendes Gomes as he admits certain players would have left regardless of cup exit
Hatters were aware of McAtee's shoulder injury before agreeing to sign Grimsby striker
Jones still keen on pushing for defensive signing ahead of deadline day
Potts determined to nail down centre half role at Luton following Naismith's exit to Bristol City
To view photographer Liam Smith’s gallery from the game, click on the link above.