Beattie proved a real thorn for the home defence all afternoon and might have finished with a hat-trick.
Before the interval he had a great shot from the edge of the box brilliantly turned away by Irishman Murphy.
And the Scunthorpe keeper denied Beattie again early in the second half from a flashing left foot shot.
Swansea looked a class act as they passed the ball around with ease.
They made certain of the points in the 67th minute when Darren Pratley released Cedric Van de Gun into the box and he finished clinically with a low shot into the bottom corner.
Scunthorpe, who had been in good form in front of their own fans, with ten points from the previous four home games, just could not get going.
They failed to muster a single worthwhile shot to trouble Dutch keeper Dorus De Vries in the visitors' goal.