Joe Garner's 71st-minute spot-kick proved the difference between the two sides as the promotion-chasing Swans were made to pay the penalty for not taking their chances.
Garner was the man brought down by Alan Tate as Scunthorpe, with the joint-worst home record in the second tier prior to kick off, claimed three crucial points to put them within touching distance of safety.
The scalp of Swansea adds to that of promotion rivals Nottingham Forest, who were undone by the same scoreline at Glanford Park only a matter of weeks ago.
It could have easily have been a different story as Swansea, on the back of four successive victories, wasted a host of opportunities, although Garner thundered a late effort off the crossbar and Lee Miller clipped a post for the home side.
Brendan Rodgers, the Swans manager, brought Leon Britton and Craig Beattie back into his starting XI, while the Iron showed four changes from Tuesday's 2-0 defeat at Portsmouth.
The high-flying visitors who dominated proceedings from the off and United goalkeeper Josh Lillis was first to be called into action, parrying Scott Sinclair's effort to safety after 11 minutes.
Scunthorpe found themselves penned in their own half, although Michael Collins should have done better with what was a weak shot when he was in space in the visitors' area.
Neat approach play looked to have handed Swans midfielder Joe Allen the opener with 25 minutes gone after he waltzed past several Iron defenders and beat Josh Lillis in what was the clearest chance of the first half, but his shot was well cleared off the line by Andrew Wright.
Garner fired straight at Dorus de Vries, but it was the visitors who continued to boss matters. Craig Beattie blazed over another great opportunity to break the deadlock when clean through.
Lillis then produced one more smart stop in the 42nd minute to keep out Nathan Dyer's drive from distance and keep resilient Scunthorpe on level terms at the break.
The Iron had the first of three penalty claims before the break when Garner went down under a challenge from Tate, but the referee did not consider a foul to have taken place.
If Swansea started the first half on the front foot, then the Iron found an extra gear at the beginning of the second.
First Wright had to be on hand to produce another timely block, this time denying Sinclair.
Sinclair mis-cued an effort before centre-back Ashley Williams volleyed over from 12 yards.
The Iron had really come back into the game but struggled to create clear-cut chances.
Swansea were left to rue their profligacy when a well-worked home attack saw Garner upended by Tate in the penalty area and he picked himself up to drill home from 12 yards.
No one came closer to a second than Garner, who smashed a shot against the top of the bar only for the rebound to come off Miller's shins and roll inches wide of a post.
There was still time for a third penalty shout of the day. Ben Gordon combined well with substitute Mark Duffy to burst into the area, the on-loan Chelsea defender looked to be clearly clipped but was shown a yellow card for diving.
He was bemused, the fans in the terrace were angry and Duffy was also booked after making his feelings known to the referee.