Both teams attempted to play the ball on the ground, however the extremely windy conditions in South Wales made that a difficult task.
A host of chances were squandered at each end before Newport went ahead through Michael Cook.
Town only half cleared their lines leaving the Exiles youngster with an opportunity to convert from close range.
Parity was restored soon after when young Glovers midfielder Gabriel Rogers curled a beautiful free kick in from 25 yards.
The Green and Whites turned the game on its head courtesy of Neville Nzembela’s tap-in.
After Devon Arnold’s shot was parried by the Newport keeper, the summer signing was on hand to score from inside the six-yard box.
But Yeovil couldn’t hold on for victory as Evan Press equalised five minutes from time.
Academy Manager Paul Wilson told YTFC.net: “It was the first game of the season and the new players are still trying to learn each other’s games.
“It was far from the complete performance we were looking for and it was disappointing to get into a winning position and not pick up three points but we’ll regroup and go again next weekend.”
The under-18s host Cheltenham Town on Saturday (11am).
Yeovil Town: Scott, Fripp, Hayes (Dix 51), Gyebi, Wan, Cherrett, Rice-Lethaby (Calverley 84), Hilton-Jones, Nzembela, Rogers (Atherly 84), Haughton (Arnold 51). Not Used: Hallett.