Paul Musselwhite's goal-kick was flicked on by Steve Torpey into the path of Paul Hayes, who cooly slotted the ball home.
Bajram Fetia had the ball in the back of the net for Rangers U21 on the ten minute mark, but saw his effort rule out for offside.
Hayes and Torpey both spurned chances to double the lead before Hayes managed to do just that in the 27th minute.
Cleveland Taylor crossed from the right for Hayes to volley home.
Tom Brighton, tipped to be returning to Glanford Park in a season-long loan, pulled one back for the Gers on 53 minutes with a curling shot from the edge of the area.
Trialist Billy Sharp restored the two-goal lead 15 minutes from time, bursting past the young Gers defence and side-footing the ball home.
Goals
SUFC: Hayes (1,27), Sharp (74)
Rangers: Brighton (53)