Iffy Onoura dropped Jamie Cureton and instead started with youth team player Jutkiewicz instead, also making his first team return after injury was Paul Smith.
It was Swindon's first trip to Scunthorpe for 21 years, and the first trip ever to their new Stadium, which looks like Walsall's new ground before Walsall extended it a couple of years ago.
Swindon started well in the first couple of minutes, but then Scunthorpe started to pile on the pressure after hitting the post a few seconds later Scunthorpe scored with a close range goal from Billy Sharp.
Then on 25 minutes Trevor Benjamin was tripped in the box, and Swindon were awarded a penalty. Benjamin took the kick and hit it down the middle, the 'keeper came close to holding the ball, but the penalty had too much power on it, and hit the back of the net to make it 1-1.
Then on 39 minutes Swindon took the lead after a corner from Gurney caused a goal month scramble and somehow Ricky Shakes found a gap to score his second goal in under a week from close range to give Swindon a rare away lead.
In the second half Scunthorpe piled on the pressure and came close to scoring a number of times with Evans being forced to make a number of good saves, and Sean O'Hanlon having to clear the ball away with a header off the line.
O'Hanlon nearly got himself sent off for an off the ball incident in which he appeared to push a Scunthorpe player to the ground, the referee missed it, but the linesman saw it. Scunthorpe were given a free kick, but O'Hanlon avoided a red card.
Charlie Comyn-Platt came on to replace Paul Smith, and Steve Jenkins replaced Chris McPhee, and late on Lee Peacock replaced young Lucas Jutkiewicz.
Scunthorpe came very close to getting a 95th minute goal with Evans having to make a very good save. Overall Scunthorpe were poor, and Swindon made the most of it with an important win by taking their chances well. This now leaves Swindon 3 points away from safety with 9 points still to play for, but other teams at the bottom keep winning as well so Swindon really need to win their last 3 games in they are to avoid relegation starting on Saturday at home to Brentford.