Jack Wilshere and Pablo Fornals both scored their first goals in Claret and Blue to help West Ham see off the Exiles at Rodney Parade.
Story of the match
The home side enjoyed the majority of the possession during the opening 5 minutes, aiming to test West Ham goalkeeper Roberto on his debut with a flurry of long throw-ins.
After 13 minutes West Ham eventually created an opportunity, summer signing Pablo Fornals hitting the post with a deflected strike from just inside the Newport area.
The Hammers managed another attempt on goal a few minutes later, good hold-up play from Albian Ajeti allowing Robert Snodgrass a shot on goal, however his effort was saved comfortably.
The Exiles should have opened the scoring when Tristan Abrahams robbed Issa Diop of possession and squared it Padraig Almond in front of goal, but the striker’s tame shot was straight at Roberto, and the tie remained level.
Despite a succession of good chances for the hosts, it was the Premier League outfit who took the lead just before half time, Jack Wilshere pouncing on a defensive error and slotting into the bottom corner to make it 1-0.
The midfielder almost got an assist one minute later, his through ball playing in Pablo Fornals, however 'keeper Nick Townsend did well to deny the Spaniard.
The League Two side should have levelled the scoring just after the interval, Abrahams inches from meeting Robbie Wilmot's dangerous low cross at the back post.
With Newport struggling to create chances, Mike Flynn made a double change 15 minutes into the second half, introducing Scot Bennett and Taylor Maloney as the home side searched for an equaliser.
However, the changes made didn't have the desired impact as West Ham doubled their advantage minutes later, Fornals tapping home from close range on 65 minutes to score his first goal for the club.
At 2-0 down the hosts still maintained a rigid defensive structure, battling well and attempting to make the most of any set pieces.
Energy levels began to decrease midway through the second half and the tempo of the game dropped as West Ham looked to maintain possession.
Wilshere made way with 10 minutes remaining as Pellegrini brought on academy graduate Conor Coventry to gain some valuable experience.
Newport almost pulled one back with five minutes remaining, however Roberto got down well to tip the header wide.
The Exiles again thought they'd scored minutes remaining, however Josh Sheehan was only able to rattle the crossbar following Coventry's mistake, and the Hammers maintained their 2-0 lead.
Jack Wilshere scores his first West Ham goal
Jack Wilshere showed great tenacity and composure to score his first goal for West Ham United in a good individual performance.
After a frustrating start to his Hammers career, the 27-year-old is tipped for a big campaign, and if he does manage to stay fit Manuel Pellegrini will have a very gifted player on hands.
Newport give good account
The League Two side gave a good account of themselves as the competed with the Hammers across the park, and went close to scoring on several occasions.
It was clear to see how the Mike Flynn's have troubled other Premier League sides at Rodney Parade, however West Ham had too much for the hosts on this occasion.
Michail Antonio picks up injury
Michail Antonio was forced off early in the first half with what appeared to be a serious hamstring injury.
The effective wide midfielder impressed after coming off the bench against Watford, and his absence will be missed in the coming Premier League games.