Connor Allan got the scoring underway early in the first half, before the young Gers took a commanding lead into the half-time interval when Chris Eadie forced a bizarre own goal from the visitors.
There was no relenting from the Light Blues after the half-time interval as Eadie got himself in on the act properly, with goals from Calum Adamson and substitute Josh Gentles putting the icing on the cake.
The result means Rangers are the only B Team remaining in the competition heading into the last 16 as League One side Stenhousemuir await in the next round.
Indeed, the Gers wasted precious little time in establishing their superiority as they cut the Highland League side open to break the deadlock.
A searching crossfield pass from Leyton Grant liberated Robbie Fraser, captain on the evening, down the left-hand side and when the 21-year-old’s delivery fizzed across the face of goal it was an unlikely source in Allan who tapped home at the far post.
It was a ferocious start from the Light Blues as both Findlay Curtis and Chris Eadie went close, while Calum Adamson fired over from Archie Stevens’ pinpoint pull-back.
And they were rewarded midway through the opening period when Curtis’ slide rule pass reached Eadie and, when the 17-year-old couldn’t quite bring the ball under control, he was given a helping hand when Fraserburgh contrived to divert the ball into their own net.
The away side were certainly throwing themselves around with a sequence of meaty challenges, but Rangers were more than a match for their experienced opponents from a physical perspective.
The second half began at a hectic pace from Rangers and they soon put the contest beyond their opponents when the lively Eadie sprung the offside trap, lifted the ball over the onrushing goalkeeper and stabbed the ball over the goalline from close range.
Rangers were purring as a result, adding a fourth of the contest shortly after when Adamson followed in his initial effort and headed home from point-blank range to leave the visitors with it all to do.
There was a special moment, too, when 16-year-old Aiden McCallion – born in the same year that Rangers reached the UEFA Cup final in Manchester – made his B Team debut in midfield.
And it was another of the substitutes, Josh Gentles, who rounded off the scoring when he latched onto a through pass beyond the Fraserburgh defence and he made no mistake in giving the goalkeeper the eyes and slotting the ball into an empty net.
RANGERS B: Munn, Allan, Grant, Nsiala, Fraser (Hutton, 77), Rice (Robertson, 30), Adamson (McCallion, 77), Lowry, Stevens, Curtis (McClure, 77), Eadie (Gentles, 61)
Subs: Halliwell, Allen, Webster, Stewart
FRASERBURGH: J. Barbour, Hay, Simpson, Young, West, Sopel, S. Barbour, Wood, Bolton, Butcher, Hawkins
Subs: Flinn, Laird, Strachan, Watt, McKay, Garden, D. Robertson, C. Robertson
REFEREE: Jordan Curran