As the game looked to be heading into half-time goalless, Padraig Amond headed home the opener from a 45th minute County corner.
With a sense of deja vu the hosts’ lead was doubled 10 minutes after the restart as Labadie converted another Newport corner.
Unable to trouble Joe Day in the home goal, the Glovers slumped to defeat in Wales confirming back-to-back defeats.
Darren Way made two changes to the side that suffered a narrow defeat to Colchester United at Huish Park a week previous.
Having served a one-match suspension, Nathan Smith returned to the heart of Town’s defence in place of Omar Sowunmi who dropped from the matchday squad in Wales.
In midfield, Connor Smith took the spot of Jake Gray who moved amongst the substitutes after a run of five games in the starting XI.
Faced with a pristine newly laid pitch at Rodney Parade, both sides enjoyed spells of possession in the opening exchanges.
Having tested the waters, it was the Exiles who produced the first meaningful attack of the game just before the 10-minute mark.
Lively from left wing-back, Dan Butler picked out Joss Labadie with a low cross, which the County captain could only blaze over from six yards to the amazement of the onlooking crowd.
After missing that gilt-edged opportunity, the hosts were almost made to pay after 20 minutes when an already diving Joe Day demonstrated his reactions to somehow get a hand to Francois Zoko’s deflected shot from 20 yards.
After flashes of excitement for both sets of fans, the game producing a stagnant period up until the stroke of half-time.
Having largely been a spectator for much of the first-half, Artur Krysiak used every inch of his 6’4” frame to stretch and tip Scot Bennett’s shot around the post for a corner.
However, the Pole’s heroics were in vain, as from the resulting corner Padraig Amond rose highest to head home former Glover Matty Dolan’s set-piece.
With no chance to respond Way’s side trudged in a goal down at the break, having battled well to contain County for much of the opening 45 minutes.
Dealt a blow at the end of the first-half the Glovers were almost dealt another just minutes after the restart.
Labadie’s stooping effort from Dolan’s wide free-kick was well kept out by the legs of Krysiak, as set plays continued to trouble Town.
Clearly buoyed by their opener, Newport went close to doubling their lead once again on 52 minutes, as Labadie’s strike from 20 yards grazed the bar on its way over.
With a sense of inevitability growing, the Exiles didn’t have to wait much longer to make it 2-0.
Producing copious balls into the box, it was from another corner that Michael Flynn’s side doubled their lead.
Dolan’s teasing delivery picked out Labadie who powerfully headed low into the ground and subsequently the back of the net to finally get on the scoresheet.
Enjoying a monopoly on possession Newport continued to dominate, as the Green and Whites struggled to find a foothold.
Entering the final quarter-of-an-hour Krysiak was once again Yeovil’s saviour as he kept out Amond’s low drive from the edge of the box, before Mickey Demetriou whizzed a 30-yard free-kick just wide.
Unbeaten at home all season, the Exiles were only threatened in injury time when Fela Olomola crashed an effort off the bar, but the Welsh outfit saw out the closing stages to condemn the Glovers to back-to-back defeats in Sky Bet League Two for the first time this season.
Newport County: Day, Bennett, Demetriou, White, Pipe, Tozer, Labadie (Owen-Evans 88′), Dolan (Rigg 69’), Butler, Amond (Reynolds 85’), Nouble.
Bookings: Labadie 28’, Dolan 45’
Subs not used: Bittner, Barnum-Bobb, McCoulsky, Jahraldo.
Yeovil Town: Krysiak, James, Nelson, N. Smith, Dickson, Bailey, Worthington (Santos 79’), C. Smith (Browne 58’), Olomola, Zoko (Surridge 52’), Khan.
Bookings: Nelson 43’, Zoko 50’
Subs not used: Maddison, Davies, Mugabi, Gray.