Graeme Murty’s team travelled to the English League One side’s Poolfoot Farm training ground for the match with James Maxwell and Jordan Houston getting on the scoresheet.
Rangers started well with Jamie Murphy working his way into the box after two minutes and cutting the ball back to Joe Dodoo but the forward diverted the ball just wide of the target.
On the 13th minute Dapo Mebude saw his shot deflected just wide of the Fleetwood goal after getting on the end of a cross from Eros Grezda.
Mebude came close again 10 minutes later as Nathan Patterson picked up a ball given away by Fleetwood. The right-back found Jamie Murphy who turned to release Joe Dodoo on the wing who found Mebude but his shot was saved well Billy Crellin.
Rangers continued to create opportunities going forward with Jamie Murphy’s corner being picked up by Graham Dorran’s who found space in the box but his shot took a deflection and was saved comfortably by Crellin.
The hosts had a chance on the half hour mark as Ched Evans made ground down the left for the visitors and cut back to Barry Baggley but he couldn’t keep his effort down as it drifted well over the bar.
Graeme Murty was forced into a substitution on the 31st minute as Jack Thomson took a knock and was replaced by Kai Kennedy.
The best chance of the first half fell the Jamie Murphy on the 35th minute as he stepped up to take a free-kick from the edge of the box and his curling effort was blocked by the feet of the Fleetwood keeper. The rebound fell to Eros Grezda but his header landed just over the bar.
Crellin was called into action again for Fleetwood just before the break as Nathan Patterson picked out Kai Kennedy in the box and his drilled effort was saved low by the keeper.
Rangers started the second-half well and Mebude had an opportunity on the 55th minutes as Nathan Patterson played him in but his shot was blocked by the keeper.
The goal did come for Graham Murty’s side on the hour mark as left-back James Maxwell cut inside and fired a shot into the back of the net from the edge of the box.
Fleetwood were denied an equaliser shorty after as Michael Fowler’s shot was blocked by the feet of Kieran Wright
Rangers doubled their scoring on the 70th minute as Eros Grezda’s corner was flicked on by Daniel Finlayson before landing at Jordan Houston who beat the keeper with his shot from inside the box.
Kai Kennedy came close to adding a third in the last 10 minutes but his shot was deflected just wide.
Rangers: Wright, Patterson, Maxwell, Finlayson, Mayo (Houston, 65), Thomson (Kennedy, 31), Grezda, Dorrans, Dodoo, Murphy, Mebude (Balde, 86). Subs not used: Budinauckas, Miller, Balde
Fleetwood Town: Crellin, Holgate, Rydel, Smith, Morgan, Hill, Matete, Garner, Evans, Saunders, Baggley. Subs: Pengelly, O’Halleron, Goldsborough, Fowler, Morris, Boyle, Johnston.