The Hornets beat Oxford United on penalties in round two to progress to this stage, while Newport have overcome Swansea City and Cambridge United in the opening two rounds.
Newport might not have been able to finish last season, but Mike Flynn's team have had an incredibly busy start to the 2020-21 campaign, already playing five matches across three separate competitions.
Indeed, they have overcome Swansea City and Cambridge United in the first two rounds of this season's EFL Cup to book their spot in the third round of the competition.
Newport also lost 1-0 to Cheltenham Town in the EFL Trophy earlier this month, but they have made an encouraging start to their 2020-21 League Two season, taking four points from their two games against Scunthorpe United and Barrow to occupy 10th spot in the table.
The Exiles lost to West Ham United in the second round of last season's EFL Cup but will be keen to continue their journey in the 2020-21 competition despite the fact that their league campaign is the priority.
Watford, meanwhile, beat Oxford United on penalties after a 1-1 draw last week to ensure that they would be present in the third round of this season's EFL Cup.
Vladimir Ivic's side will be looking for an immediate return to the Premier League, but the Serbian has assembled such a big squad full of quality, meaning that a run in this competition would be welcomed.
Watford actually reached the fourth round of last season's EFL Cup before losing to Everton and will certainly be the favourites to progress from Tuesday's tie at Rodney Parade.
Newport County EFL Cup form: WW
Newport County form (all competitions): WLDWW
Watford EFL Cup form: W
Watford form (all competitions): WWD
Newport boss Flynn is expected to again line his side up in a 3-5-2 formation on Tuesday, but there will be changes from the team that started in the league against Barrow on Saturday.
That said, the back three could remain unchanged from Saturday, with Brandon Cooper keeping his spot.
As for Watford, Andre Gray, Isaac Success, Ismaila Sarr and Gerard Deulofeu are still on the sidelines through injury, but there are expected to be wholesale changes from the side that faced Wednesday.
The XI will have a familiar look to the one that started against Oxford in the last round, although there could be a change in midfield with on-loan Manchester United youngster James Garner coming in for his full debut.
Newport County possible starting lineup:
King; Howkins, Cooper, Demetriou; Shephard, Willmott, Sheehan, Twine, Haynes; Amond, Abrahams
Watford possible starting lineup:
Bachmann; Navarro, Sierralta, Agyakwa, Wilmot, Stevenson; Phillips, Garner, Quina; Sinclair, Perica
We say: Newport County 1-2 Watford
Newport are certainly capable of making it an uncomfortable night for Watford, but it is difficult to look past the Championship outfit, who will be able to put better quality on the field. We are not expecting a comfortable away success but fancy the Hornets to progress to the fourth round of the competition.