Newport goalkeeper Joe Day provided the heroics to see the Exiles come away from Huish Park 2-0 victors.
Looking to get back to winning ways in Sky Bet League Two, Town enjoyed the better of the opening 45 minutes with Connor Smith and Omar Sowunmi both going close.
The hosts remained on top after the break but fell behind on 57 minutes when former loanee Josh Sheehan converted a flowing move.
After an already impressive first half the seemingly unbeatable Joe Day produced two stunning saves to deny Francois Zoko an equaliser, before Paul Hayes rounded off the win in second half stoppage time.
After suffering a narrow Checkatrade Trophy semi-final defeat at Shrewsbury Town in midweek, Darren Way made two changes for the return to league action.
Reverting to a more familiar 4-4-2 formation, Sam Surridge and Lewis Wing came in for Oscar Gobern and Jared Bird, as the former dropped from the matchday 18.
Missing out through illness Alefe Santos dropped from the squad along with Ryan Seager as the sixth loan, meaning Marcus Barnes was involved for the first time since mid-January following an ankle injury.
Looking to replicate their early February form which saw four straight wins at home, the Glovers started in positive fashion with two early chances.
Enjoying a spell of dominance, Connor Smith almost opened the scoring when his quickly taken free-kick from 30 yards had to be tipped round the post by a scrambling Joe Day.
From the resulting corner, the Exiles 'keeper was called into action once again reacting well to palm away Omar Sowunmi's header.
The early opportunities pathed the way for a first-half of relative dominance for the hosts who stroked the ball about competently in a show of confidence.
Strike duo Surridge and Francois Zoko both looked menacing in the final third, but Town couldn't call Day into further action as Newport registered their first meaningful attempt on goal with 36 minutes on the clock.
Former Town duo of Josh Sheehan and Matty Dolan combined at a corner, with the latter's miss-hit volley being flicked goalwards by Padraig Amond who tested the reflexes of Jonny Maddison between the sticks.
That was as good as it got for the Welsh outfit in the first half as the Green & Whites remained on top, only lacking an opening goal from an otherwise dominant display.
Keen to turn territory into the lead Way's side continued where they left off after the break.
Captain Zoko twice went close to opening the scoring, whilst at the other end Robbie Willmott pulled a driven strike just wide as the game started to open up.
With the hosts still in control a Newport opener seemed unlikely, but against the run of play Mike Flynn's side broke the deadlock.
Ben White's pull-back picked out Sheehan in the middle, which the former Swansea midfielder competently swept into the far corner in front of the travelling fans.
Looking for an immediate response, Day had to be at his best once again to keep out Town's captain, when he raced from his line to block Zoko's shot from close range.
Becoming a personal duel between the two the County stopper produced another stunning save on 67 minutes, somehow getting a hand down low to push away the striker's well-directed header.
Emptying the bench of attacking options the Glovers switched to 4-3-3 for the final 10 minutes, committing numbers forward.
However, with Newport camped in their half to defend their lead Way's side couldn't find a way through and were dealt a sucker punch when Hayes coolly converted a second with numbers scarce at the back for Town.
Yeovil Town: Maddison; Whelan, Sowunmi, James, Dickson; Green (Browne 70'), Wing, C. Smith, Khan (Fisher 77'); Surridge (Barnes 59'), Zoko.
Bookings: Zoko 45'
Subs not used: Nelson, Mugabi, Donnellan, Bird.
Newport County: Day; Willmott (Collins 84'), White, Tozer, Demetriou, Butler; Labadie, Dolan (Bennett 81'), Sheehan; Hayes, Amond (Nouble 56').
Bookings: Hayes 66', Labadie 83'
Subs not used: Bittner, Jackson, Reid, McCoulsky.