Dominating from start to finish the young Glovers had to wait until the 86th minute to break the deadlock, with Nzembela lobbing away stopper Fraser Thomas.
Standing firm until full time, Antonio Falanga’s side picked up an impressive win in front of the home faithful to progress.
Gracing the Huish Park pitch for the first time this season, the Under-18s were without suspended duo Jeremiah Gyebi and Joe Tomlinson.
Thomas Hayes came in for Gyebi, while Lewis Dix slotted in at left-back in place of Tomlinson.
Enjoying a monopoly on possession from the off, Town went close inside the opening five minutes when Jake Rice-Lethaby’s mazy run and cross narrowly evaded the boot of Paulius Golubickas.
It was Rice-Lethaby who produced the game’s first shot on goal, collecting from Golubickas before driving a low effort just wide from the edge of the box.
The same duo combined once more, as Thomas raced from his line to smother Rice-Lethaby before jumping to his feet to deny Golubickas on the rebound.
Only missing the finishing touch in the final third, the junior Green and Whites went close again midway through the first half, when Gabriel Rogers cleverly cut inside from the right before curling an effort just over.
Unable to get out of their own half, Bishop Sutton remained on the defensive until the break and could only watch as Yeovil captain Samyan Ismail drove into the area and drilled a low shot inches wide.
Town had the ball in the net on 54 minutes when Rogers converted Golubickas’ through ball, only for the linesman’s flag to deny a deserved opening goal.
Only looking to threaten the Yeovil goal from set-pieces, Nathan Rendell glanced a header wide from a corner as the game looked to be heading towards a goalless 90 minutes.
However with a little over 10 minutes remaining, Nzembela replaced Nestor Sako before netting the winner soon after.
Latching on to Brad Cherrett’s lofted ball over the top, the striker coolly looped an effort over Thomas having spotted the keeper off his line.
With little time to respond, the visitors couldn’t test Tommy Scott in the home goal allowing Falanga’s side to see off their Western League opponents to reach the second round.