Tommy Wilson took a squad with an average age of just 18 to Central Park and was delighted to secure a victory.
Calum Gallagher's penalty was enough to secure the win as the striker grabbed a sixth goal in five competitive matches this season.
The home side included a number of players with First Division experience this season and it showed in a tight first half.
Francesco Stella tested the Blue Brazil's keeper with an early free kick, but it was comfortably held.
Young midfielder Charlie Telfer then attempted to test the keeper from distance after a decent exchange with Stella mid way through the first half.
However Rangers came closest when Andy Mitchell's cross was spilled and almost sneaked in at the far post just after the half hour mark.
Gallagher was feeding off scraps through the first period and the one time he was given something to run on to the linesman's flag was quickly up to signal offside from Stella's pass.
The striker did have the ball in the net in the early part of the second half but he was again flagged offside.
Stella then stung the palms of the home side's keeper again before Darren Ramsay slammed the rebound in to the side netting with the flag up once again.
The visitors were beginning to exert some pressure and it paid off just before the hour mark when Telfer skipped in to the box and was felled before he could get his shot away.
Gallagher quickly grabbed the ball under encouragement from Wilson and his finish from 12 yards was expert.
The home side tried to rally and they might have drawn level but for some slack finishing and last gasp defending from the Light Blues.
Wilson's side weathered the storm and might have extended their lead late in the game when Stella was stopped by a smart save after he was well played in by substitute Jamie Burrows.
It was far from a vintage performance from Rangers but it left Wilson satisfied by the manner in which his young side dug in.
Rangers: Gallacher; Mitchell, Gasparotto, Hegarty, Wilson; Wiktorski, Urquhart (Fotheringham 58); Ramsay (Burrows 73), Telfer (Halkett 75), Stella; Gallagher.
Subs: Currie, Gibson.