Victor Moses and Soares combined to give the home side a 21st-minute lead.
Moses then flashed a 20-yard shot over the bar and went even closer on the half-hour mark when his long-range shot forced a fine save from goalkeeper Joe Murphy.
The visitors went close to levelling when Jonathan Forte headed a cross from Ian Morris over the bar.
Moses then scampered away down the left again and fired over a pin-point cross for Morrison to head beyond Murphy on 39 minutes.
Scunthorpe refused to go down without a fight, but could only muster a weak Andy Butler header between the restart and the hour-mark.
Late on Curtis Weston appeared set to reduce the deficit for the visitors, but Clint Hill denied the sub.