Town boss Paul Hart made five changes to the side that lost at home to Notts County on Saturday, with an immediate return to the side for Andy Frampton after his one-match suspension. Phil Smith replaced injury victim David Lucas in between the sticks with Simon Ferry handed a rare start in midfield. Alassane N'Diaye, on loan from Crystal Palace, made only his second start with Jon-Paul McGovern dropping to the bench alongside Calvin Andrew who was replaced by Elliot Benyon in the frontline.
Early chances fell for both sides inside the opening five minutes with Sheffield Wednesday frontman Neil Mellor rolling an early effort just side before Matt Ritchie shot straight at Nicky Weaver from the edge of the box.
Town forced their second corner of the game inside seven minutes following good work from Simon Ferry, making his first start since the home clash with Walsall in early March. Ferry's ball through found Ritchie who did well to earn the set-piece.
It was a composed, impressive start from Swindon who enjoyed much of the possession inside the first fifteen minutes with Elliot Benyon and Ritchie looking bright in the forward line.
Town's start came crashing down on 16 minutes with the home side opening the scoring. A low strike from the edge of the box by Darren Potter took a wicked deflection off Lecsinel Jean-Francois and rocketed past Phil Smith into the back of the net.
Moments later the Robins could have been level, but Ritchie - having been played through - rounded Weaver only for the 'keeper to get back and regain possession just as the frontman was going to roll the ball into the empty net.
The home side extended their advantage on 27 minutes with a well-taken header from Mellor. A deep cross from right-back Jon Otsemobor from close to the half-way line saw Mellor get the better of Frampton and loop a header home from 16-yards out. Chances came Swindon's way after the goal with Frampton and Benyon twice denied by superb goalkeeping from Weaver.
Town's afternoon then went from bad to worse with Frampton going down under a heavy challenge, injuring an ankle, before being replaced by Scott Cuthbert in the heart of the backline.
Swindon got a goal back three minutes before the break with a superb first goal in a Town shirt from Jonathan Douglas. The skipper followed up a blocked shot from Ritchie to fire in a right-footed effort into the top corner of the net from 25-yards.
After four minutes of added time, Town went into the break with renewed hope ahead of the second period.
Despite making a strong start to the half, Paul Hart's side edged closer to relegation to League 2 as defensive hesitancy from Scott Cuthbert and Michael Rose allowed Neil Mellor to place the ball past Phil Smith at the second attempt just before the hour mark to make it 3-1.
The visitors continued to strive for a second goal to give them a glimmer of hope, and despite efforts from Elliot Benyon and another long range punt from Douglas, they couldn't get themselves back into the game.
As the match drifted towards its final stages, Town's stay in League 1 was minutes away from ending, and with the final whistle, relegation to the Football League's fourth tier was confirmed.