Goals from Nestor Sakoand Jack Rice-Lethaby earned the young Glovers three points against a Robins side who were yet to drop points in the EFL Youth Alliance.
The first half brought few chances for either team but after the interval, Yeovil dominated and deservedly took the lead on the hour.
Samyan Ismail and Gabriel Rogers pressed deep in Swindon territory with the latter stealing the ball, driving into the box and pulling back for new recruit Sako to score.
Six minutes later, the hosts wrapped up proceedings through Rice-Lethaby’s first of the campaign.
A mistake in the visiting ranks saw the midfielder race on to a loose ball and he coolly dispatched underneath the away keeper to seal victory.
The Under-18s are next in action against Oxford United on Saturday, September 16th.