Swansea's hero was Frenchmen Willy Gueret who not only pulled off two brilliant close-range saves but stood up well to stop the vastly experienced Peter Beagrie from scoring from the penalty spot.
Scunthorpe cracked the Swansea defence in the opening 40 seconds, Cliff Byrne and Matthew Sparrow had initially carved out the opening and then it was Paul Hayes who swept the ball to the left for Steve Torpey to tap home.
That gave the game a great impetus and after Richard Kell had fired over for Scunthorpe, Adrian Forbes rifled over from 30 yards for the visitors and Kevin Nugent headed into Paul Musselwhite hands.
However Scunthorpe were in dominant form and Beagrie was denied by the woodwork and he followed up by forcing Gary Monk to head off the line.
Ian Baraclough was caught out by Forbes and Musselwhite had to come off his line swiftly to clear.
Gueret was then called into action producing two great saves first diving to his right to turn around a Baraclough free-kick and followed up with a point blank stop from Richard Kell.
Beagrie then crashed the ball against the woodwork the second time and Matt Sparrow twice tested the visiting defence with excellent runs.
Scunthorpe should have wrapped up the game when they were awarded a 67th-minute penalty, Gueret brought down Baraclough and referee Mason immediately pointed to the spot but the keeper redeemed himself by making a fine save.
In the closing stages Torpey was denied a second goal when he hit the woodwork and both Hayes and Sparrow had efforts blocked on the line.