After a first-half largely devoid of final third action, the Welsh outfit took the lead just before the hour-mark courtesy of a pinpoint Mickey Demetriou free-kick.
Nathan Smith had Town’s best chance in the closing stages with a shot from close range, but County held on for a win that pulls the Glovers into the scrap for safety.
With every outfield player available for selection, Darren Way made five changes to the side that lost out to promotion chasing Portsmouth six days ago.
Despite the relative fit bill of health, one alteration was forced with the ever-present Artur Krysiak ruled out with a training ground foot injury forcing Jonny Maddison to make his EFL debut.
After coming off the bench in Hampshire to mark his return from almost three months out with an ankle injury, Otis Khan replaced Tom Eaves in the Glovers front three.
In a second attacking change, Omar Sowunmi came in for Brandon Goodship in a bid to combat the challenging Rodney Parade conditions, with two further alterations in defence.
With much made of the importance of the fixture before kick-off, Smith returned to make his 250th Yeovil appearance and take the captain’s armband, whilst Ryan Dickson recovered in time from an ankle knock to replace Tom James at left-back.
On a pitch dominated by a combination of mud and sand as opposed to the usual green expanse, it was an unsurprisingly scrappy start to proceedings.
Perhaps more used to their surroundings, it was County who dominated proceedings in the opening half an hour with an early chance for Alex Samuel.
Chasing a ball over the top, the Newport striker beat the onrushing Maddison to the ball but saw his attempted lob from just inside the box drift over the bar, with the eventual collision between the two not meriting a spot kick in the eyes of the officials.
With the home support encouraged by their side’s start it took until 19 minutes for Town to create a nervy moment for the hosts, as Alex Lacey’s header from a Khan free-kick had to be tipped over for a corner by stopper Joe Day.
It was a rare foray into the Newport final third for Way’s side, with their only other opportunity coming from the lively Zoko’s lay-off for Khan whose eventual shot was blocked for a corner.
Although Newport enjoyed plenty of time in the Glovers half, Maddison remained largely untroubled between the sticks, only being called on to routinely claim Ryan Bird’s header with a little over five minutes of the half remaining.
As the first-half drew to a close it was the former Yeovil striker who was at the heart of the action as he had a penalty claim waved away by referee Dean Whitestone having gone down under challenge from Smith.
The incident rounded off the first-half proceedings, with Newport unable to turn territory into goal scoring opportunities.
With the home outfit making a substitution at the break both sides lined up with variations on 4-4-2 after the restart, with Town starting the half brightly.
After good work from Zoko to recycle possession, Butcher’s ball into the box found Khan who weaved his way into a shooting position, only for the livewire’s effort to drift over the bar.
In the 15 minutes after the restart the Glovers enjoyed an even share of possession arresting the pattern of the first-half, only to be dealt a huge blow by the set-piece expertise of Demetriou.
After Bird was brought down 25 yards from goal, the defender stepped up to expertly dispatch an effort into the bottom corner to send the home crowd into raptures.
The opener instantly saw Akpa Akpro introduced for Khan, before Shayon Harrison took to the field in place of Sowunmi shortly after as Town re-jigged their frontline in search of a response.
Committing numbers forward Newport always looked likely to threaten on the break, and perhaps should’ve put the result beyond doubt with Sean Rigg and Samuel both going close.
With the deficit only one, Town always had a chance to rescue something from their trip to Wales and could’ve done so when Akpa Akpro headed wide from Harrison’s flick-on with Day stranded.
In the process of heading wide the Town striker picked up a lengthy facial injury which meant the Glovers played much of the final 10 minutes with 10 men, as it all seemed to conspire against Way’s side.
With the last kick of the game Smith prodded an effort just over the bar after a scrap in the box, but Newport stood firm to leave Yeovil hovering just four points above the drop zone.
Newport County: Day; O’Brien (Rigg 45’), Bennett, Demetriou; Pipe, Rose, Randall (Jones 86’), Owen-Evans, Butler; Bird, Samuel (Williams 90’).
Bookings: Randall 45’.
Subs not used: Bittner, Barnum-Bobb, Myrie-Williams, Gordon.
Yeovil Town: Maddison; Shephard, Lacey, Smith, Dickson; Dawson, Butcher (Lawless 76’), Dolan; Khan (Akpa Akpro 61’), Sowunmi (Harrison 67’), Zoko.
Bookings: Khan 45’.
Subs not used: Mugabi, James, Goodship, Eaves.