Craig Beattie opened the scoring with a precise free-kick in the first half, the striker's third goal in his last four games.
Former Ajax forward Cedric Van der Gun gave the Welsh side breathing space with a second goal after the break and the Swans never looked like surrendering their advantage, as they kept a fifth clean sheet in their last six games.
Swansea immediately stamped their authority on the game and they were nearly in front just five minutes in but Joe Allen fired wide of Joe Murphy's goal.
The Welsh side's crisp passing and movement was proving to be too much for Scunthorpe and the visitors fashioned another goalscoring opportunity but Beattie fired wide from 25 yards out.
The former Celtic striker spurned another chance after 18 minutes, but scuffed his right-footed shot after a defensive error.
But the big striker made amends 31 minutes in, firing a free-kick beyond Murphy and into the bottom-right corner of the net from 25 yards out.
Scunthorpe's supporters were becoming disgruntled as Swansea remained on the front foot.
Van der Gun was proving to be a handful and the Dutchman set up Beattie, who was denied a second goal by a fine fingertip save by Murphy.
Scunthorpe never got into their stride in the first half, with Swansea proving to be difficult to break down.
Michael O'Connor had a half chance on the stroke of half-time but his right-footed volley was comfortably dealt with by Dorus de Vries.
The visitors started where they left off after the break and after some good work from Thomas Butler on the left, Beattie found space in the area before unleashing a left-footed drive which was superbly save by the agile Murphy.
The Iron showed more desire in the second half and started to ask some questions of the Swansea defence.
Gary Hooper raced away down the left but misplaced his pass to strike partner Paul Hayes.
But the home side were caught out after 67 minutes when Darren Pratley broke from midfield and fed Van der Gun, who raced in on goal and produced a clinical right-footed finish which went in off the post.
Van der Gun looked to have been brought down in the penalty area 12 minutes from time, but referee Karl Evans booked the forward for diving.