Mauricio Pochettino - overseeing his 200th match in the Spurs dugout - watched on as an own goal from Dan Butler and a well-taken effort from Erik Lamela got the job done against the League Two outfit.
Spurs will now travel to Rochdale in the last 16 of the competition on February 18.
Find out how all of the action unfolded in North London courtesy of Sports Mole's minute-by-minute updates below.
TOTTENHAM HOTSPUR SUBSTITUTES: Gazzaniga, Trippier, Sanchez, Walker-Peters, Eriksen, Alli, Kane
NEWPORT COUNTY SUBSTITUTES: Bittner, Dolan, McCoulsky, Reid, O'Brien, Sheehan, Hayes
TOTTENHAM HOTSPUR XI: Vorm; Aurier, Alderweireld, Foyth, Rose; Wanyama, Winks, Sissoko, Lamela, Son; Llorente
NEWPORT COUNTY XI: Day; Pipe, White, Demetriou, Butler; Tozer, Bennett, Labadie, Willmott, Nouble; Amond
If you would like to read our on-the-whistle match report, you can do so by clicking here. Goodbye for now.