Goals from Dion Charles and Colby Bishop either side of a Brett Pitman strike settled the tie in Accrington's favour.
The hosts posed the early threat and nearly took the lead through right-back Michael Nottingham. A corner was put on the penalty spot, Nottingham rose highest, but couldn’t convert the header.
Two minutes later, Town were made to pay when Colby Bishop headed back across goal for Dion Charles to head into an empty net.
The lads almost equalised immediately when Ellis Iandolo’s cross was cleared by a Stanley body. Twine hit an incredibly sweet volley that was inches from finding the top corner.
Had it done so, would certainly have been a contender of Goal of the Season.
The Gaffer was forced into his first change of the afternoon when Jonathan Grounds went down following an interception on a Dion Charles cross. Jordon Garrick was the player to replace the centre-back.
On the half-hour mark Town struck back through Brett Pitman. Akin Odimayo played a lofted pass over the Accrington defence and the striker looped the ball over an on-rushing Toby Savin.
Two minutes later it was Twine again who put fear in the Accrington hearts, when his dipping free-kick crashed off the crossbar and then off the back of Savin.
Centre-back Mark Hughes was lucky to escape a second-yellow card following a late challenge on Twine in the middle of the pitch.
The hosts then took the lead fro the second time when a corner went all the way through and was headed in by Bishop at the back post.
After the break, it was a forty-five minutes that yielded few chances for either side in an attempt for the lads to get back into the game.
Jordon Garrick won the ball just outside Town’s penalty area and carried it with intent towards the Accrington box.
He tried to find Hallam Hope who made an angled run into the area, but the pass bounced between Hope and a Stanley defender and was cleared to safety.
Despite three changes from Town, they still couldn’t manage to find their way through a resolute defence.
Although the hosts held firm, there was one last chance for Swindon when Scott Twine got a shot away from an angle, but Savin was there to parry the effort away.
In the dying embers of the match, Accrington had a great chance to put the game to bed when Matt Butcher cracked a shot against the crossbar, from just outside the box.
The lads play host to Oxford United on Tuesday night in another important League One fixture.