The vastly experienced Trevor Benjamin was a key man for the Robins as he fought hard for every ball, often theatrically, but he was a constant thorn in the home defence and skipper Sean O'Hanlon gave little away at the back.
Ian Baraclough was a busy midfielder for the Iron while the introduction of Matthew Sparrow brought a little more urgency in the late stages to try and keep the vigor of Andy Keogh and Billy Sharp in action but without success.
After a tentative start, Scunthorpe settled and it took a brave save from Rhys Evans, diving at the feet of Keogh to keep the Robins goal intact.
However the home side captalised in the eighth minute, when following a corner, the ball bounced around in the area before Sharp pounced to force home his 22nd goal of the season.
Cleveland Taylor was on target for the Iron but Evans was not troubled and then at the other end, Tom Evans dealt easily with Toumani Diagouraga's effort.
Swindon levelled matters in the 26th minute. Andy Crosby brought Diagouraga down in the box and Benjamin's powerful left foot shot from the penalty spot just evaded Tom Evans.
Scunthorpe seemed to lose their way after that setback and they found themselves behind six minutes from the break when Ricky Shakes forced the ball home from close range.
The Iron dictated most of the second half with Rhys Evans having to be alert early on to hold threats from Keogh and Steve Torpey.
Keogh was inches wide on the hour mark and Sharp forced another excellent save and then saw O'Hanlon head off the line.
Peter Beagrie tested the Robins keeper with six minutes left, a teasing free kick being clutched under the bar and Richard Hinds had a good chance in the last minute when set up by Keogh but his effort was straight at Rhys Evans.