The goals came from David Edgar in the first half and Ashley Williams and Shefki Kuqi after the break.
The Swans also created a new club record with their 23rd clean sheet of the season.
Angel Rangel brought a smart save from Iron keeper Joe Murphy in the fourth minute just after Paul Hayes had fired inches wide of the Swansea net.
Two minutes later, a cross from Mark Gower was turned onto the crossbar by Kuqi as the Swans piled on the early pressure.
The recalled Joe Allen then sent Kuqi unmarked down the middle but he failed to control the ball and Murphy went down to save his low shot.
Murphy was back in the action in the 16th minute diving to save a weak header from Guillem Bauza, who was unmarked in the centre of the goal.
The goal the Swans deserved came in the 27th minute when Edgar was left unmarked at the far post to head in a David Cotterill corner after Kuqi's faint touch on.
Bauza missed another chance from a central position just before the break when he sent a snap-shot wide after the visitors defence had failed to clear.
Five minutes after the break the Swans doubled their lead and once again it came from a Cotterill corner.
The Iron defence had plenty of time to clear the ball but it bounced around their goal until Williams stuck out a foot to poke it into the net.
It was one-way traffic and a Cotterill cross was turned goalwards by Kuqi only for Murphy to turn and gather before it crossed the line.
Nathan Dyer smashed in a shot but Murphy reacted smartly to clutch and one minute later he had another effort cleared off the line by Michael Raynes after Kuqi had broken away and passed inside.
Kuqi made it three in the 80th minute when Raynes headed a cross into his path and he ran on to easily beat Murphy with a low shot.
The nearest the Iron came to troubling the home goal came in the 86th minute when Josh Wright hit the top of the crossbar with a free-kick.