The Light Blues were on top in the first half after racing out of the blocks quickly, but they had little to show for their early superiority when the half-time whistle blew.
However, they wasted precious little time in turning the currency of chances into goals after the interval, as strikes from Kristian Webster and James Graham proved the difference.
Indeed, it was a young Rangers side that took to the pitch in Lancashire, with six players eligible to play Under-18s football starting from the off.
Among those introduced to the starting lineup were Chris Eadie and Calum Adamson, both born in 2007, with the latter making his first appearance for the B Team.
And both players certainly made their presence felt in a first half that Rangers controlled.
Robbie Fraser was first to test his luck in the contest as his curling effort on his weaker side drew a fantastic stop from Jack Flint at full stretch.
The away side ought to have broken the deadlock soon after when Archie Stevens raced clear down the right-hand side, but the 18-year-old was denied when his low, driven finish was thwarted by the feet of the Bolton goalkeeper.
The opportunities continued to come for the visitors, with Graham manufacturing a decent opportunity when he raced clear of the Bolton defence and his finish was lifted over the crossbar.
Rangers upped the intensity further as the half-time interval drew closer, with Graham once again denied when he was picked out by Paul Nsio inside the penalty area.
Quality was what was required from the young Gers in the second half, and the side answered the call when the deadlock was broken eight minutes into the second period.
A short corner caught the home side on the hop, creating the space for Cole McKinnon to deliver a dangerous cross into the penalty area that crept through to Webster at the far post who unleashed an unstoppable strike into the bottom corner.
That spiked the confidence levels of the Light Blues in the contest as they stretched their advantage five minutes later. Nsio was the architect as the 17-year-old stabbed a delightful pass into the forward who controlled impeccably, produced a spin to match, and lashed a terrific finish off the underside of the crossbar and over the goal line.
Stevens continued to wreak havoc down the right and he almost got on the scoresheet just beyond the hour-mark when his finish from a tight angle flew off target.
There was also an effort from a free-kick on the edge of the penalty area that substitute Zak Lovelace almost wrote his name on, with Flint springing down low to tip the Englishman’s effort around the post.
Rangers stood tall as Bolton threw bodies forward in the latter stages, although the home side only had a Matthew Tweedley chance to show for their efforts in the second half.
David McCallum rung the changes with eight minutes remaining as Cameron Scott, Jack Wyllie, Findlay Curtis and Kieron Willlox were introduced, the former two being only 16 years of age.
It was invaluable experience for all four players as the game ticked towards its conclusion and an especially young Gers picked up a valuable victory in Lancashire.
BOLTON WANDERERS B: Flint, Matheson, Halford, Trialist, Inwood, Frimpong, Tweedley, Sharples-Ahmed, Loureiro, Trialist, Lockett
Subs: Dallimore, Westwood, Lewis, Fleury, Abimbola, Tutte
RANGERS B: Munn, Hutton, Webster (Wyllie, 82), Allan, Fraser, McKinnon, Adamson (Ishaka, 68), Nsio (Curtis, 82), Graham (Scott, 82), Stevens (Willox, 82), Eadie (Lovelace, 53)
Subs not used: Halliwell