Second-half goals from Steven Alzate, Matt Taylor and Elijah Adebayo proved the difference at Huish Park in this all West Country affair.
Following Town’s 6-0 win at Newport last weekend, their biggest ever in the EFL, manager Darren Way was forced into one change; Middlesbrough loanee Enes Mahmutovic made his Glovers debut having returned from international duty with Luxembourg, replacing the injured Gary Warren.
It was a straight swap as Mahmutovic came in to partner Omar Sowunmi at centre-back. Tom James was back on the bench after a month out with a hip problem in place of Omari Patrick, who was the unfortunate sixth loan.
Stuart Nelson (calf), James Bailey (knee), Francois Zoko (knee) and Wes McDonald remained sidelined through injury.
Alex Pattison received an early booking with four minutes on the clock as he pulled back Keshi Anderson.
Eight minutes in Town set a new record in the EFL, having not conceded for 522 minutes since the home draw with Mansfield in August.
Swindon looked to test that resolve as they put in a couple of early crosses but the new central defensive partnership of Sowunmi and Mahmutovic stood strong.
Mahmutovic was soon involved again, stretching full length to brilliantly deflect Elijah Adebayo’s goalbound effort onto the woodwork.
From the resulting corner, Swindon captain Ollie Lancashire poked wide following a goalmouth scramble.
Town’s Bevis Mugabi was the next player to enter the book after a mistimed challenge on Adebayo having lost possession in a dangerous position.
Steven Alzate’s subsequent free-kick caused some problems in the Glovers defence as Adebayo’s eventual header landed on the roof of the net.
Swindon had started the brighter without testing Nathan Baxter, while Town were struggling to get their quick, attacking passing game together on a slippery surface against a well-organised side.
The away side continued to come forward and Baxter was sent scrambling as Anderson’s audacious lob went just over from the edge of the area.
At the other end, Diallang Jaiyesimi’s pace was causing some problems for Swindon’s defence and his great run saw the ball eventually fall to Pattison, who fired over from range.
The Glovers started to break forward with more regularity, first Carl Dickinson’s free-kick found Alex Fisher whose header lacked the power to test McCormick, before Jordan Green’s shot was well claimed by Luke McCormick in the away goal.
A minute shy of the break Marc Richards looked to break through on goal but Sessi D’Almeida was there to make a crucial interception before coming away with the ball.
In the final minute of first-half stoppage time, Fisher looked to put Yeovil on the front foot, beating Luke Woolfenden on the left before delivering a dangerous cross that Green was inches away from making a good connection.
Swindon remained on top at the start of the second half as Baxter did well to palm Anderson’s venomous shot over the bar as he cut in from the right but could do nothing minutes later as Swindon took the lead.
Alzate 25-yard strike flew into the left-hand bottom corner on 59 minutes, the first goal the Glovers had conceded in 573 minutes.
Sowunmi was booked as Swindon looked to press home their advantage before the big central defender slipped at the back but did just enough to put off Anderson as Baxter came out quickly to block.
Way made a trio of attacking changes throughout the second half as Olufela Olomola, Rhys Browne and Jake Gray came on to try and change the game.
With 11 minutes remaining, Matt Taylor fired home a long-range free-kick to double Swindon’s advantage.
Town had a great chance to halve the deficit as Anderson pushed Green over in the area but Olomola’s penalty clipped the top of the bar.
Minutes later, Adebayo cut in from the right and fired home into the right far corner with just over a minute remaining to increase Swindon’s lead and condemn Town to a 3-0 defeat.
Yeovil Town (4-4-2): Baxter; Mugabi, Sowunmi, Mahmutovic, Dickinson; Green, Pattison, D’Almeida, Arquin (Gray 80’); Jaiyesimi (Olomola 56′), Fisher (Browne 68’).
Bookings: Pattison 4’, Mugabi 18’, Sowunmi 67’.
Subs not used: Phillips, Rogers, James, Donnellan.
Swindon Town (4-3-3): McCormick; Woolfenden, Nelson, Lancashire, Taylor; Dunne (Smith 88), Diagouraga, Alzate (McCourt 84); Anderson, Richards (McGlashan 73’), Adebayo.
Bookings: Adebayo 89.
Subs not used: Vigouroux, Iandolo, Twine, Romanski.