Remaining top of the table, Town bounced back from the disappointing 3-0 Youth Alliance Cup defeat at Oxford in midweek to continue their superb league form.
Making a lethargic start in Wiltshire, the visitors had goalkeeper Tommy Scott to thank for a string of fine saves to keep the score 0-0 early on.
Growing into the match the Glovers began to cause Swindon issues with the lively duo Nestor Shako and Devon Arnold looking causing the hosts all sorts of problems with their close control and direct running.
In fact, it was Shako who opened the scoring just before the half-hour mark, a lead that Town would comfortably take into the break.
Making a change in midfield at the halfway stage the green and whites dominated after the restart and soon doubled their advantage.
Shako grabbed his second of the match to take his tally for the season to three.
Having worked tirelessly all game, Neville Nzembela was replaced by Archie Sturdy midway through the half to allow Arnold to take up the central striker role.
However, with 15 minutes remaining Town’s striker received a straight red card for a dangerous tackle which saw a switch to a 4-4-1 formation.
A tireless work rate from the players left on the pitch ensured the Robins were unable to make their man advantage count, as Yeovil ground out a 2-0 win to ensure their impressive start to the campaign continued.