Five goals were plundered in a thrilling first 45 minutes, with a brace from Zander Hutton, alongside strikes from Findlay Curtis and Paul Nsio, cancelled out Tate Xavier-Jones’ early opener.
The English visitors responded confidently in the second through goals from Jamie Odegah and Dylan Stitt to threaten a comeback, but the Gers stood tall to close out the triumph.
The young Gers were boosted by the inclusion of both Curtis and Nsio from the off, while Hutton has enjoyed regular first-team exposure in recent months.
However, the Light Blues got off to a nightmare start when the visitors broke the deadlock inside two minutes as Tate Xavier-Jones finished off a sweeping counter-attack despite the best efforts of Mason Munn.
The setback did seem to spark Rangers into life, who found the leveller eight minutes later when Curtis and Nsio combined on the edge of the penalty area and the latter arrowed a cultured finish low into the bottom corner.
And the game was soon completely turned on its head when Rangers concluded the turnaround less than 60 seconds later.
Hutton found himself advanced in the penalty area from his right full-back position and, when his delivery found its way to Curtis at the far post, the 18-year-old flashed a half-volley into the bottom corner.
Every wave of Gers pressure seemed to be cue panic stations in the Luton ranks, who were counting the cost on the half-hour mark as the Light Blues added a third of the afternoon.
It was fantastic combination play in the final third which proved the away side’s undoing, allowing Chris Eadie to punch a delightful pass through to Hutton who, with only the goalkeeper to beat, made no mistake in slamming his finish low and into the far corner.
The wave of relentless pressure continued from Rangers and, with that, so arrived the fourth goal of a manic first-half.
Curtis was the architect on this occasion, driving at his marker and lifting a hopeful cross towards the far post in which Hutton arrived on the opposite side to crash a thunderous first-time finish in off the inside of the post.
A fifth goal didn’t appear out of the realms of possibility given the fluid nature of the hosts’ performance; Curtis opening his body and guiding a dangerous effort into the arms of Liam Coyne in the Luton goal on the stroke of half-time.
Rangers began the second half in the same manner as the opening period, with Eadie going close from the edge of the penalty area.
At that point it appeared that the Light Blues were in cruise control, but they were rocked on 57 minutes when Jamie Odegah sprung the offside trap and had the whole of the Rangers half to compose himself and finish beyond Munn.
It proved the cue for Smith to introduce Cameron Scott in place of Kerr Robertson as Rangers sought an avenue to reaffirm their control.
However, the Hatters put the cat among the pigeons six minutes later as they found a third of the afternoon when Dylan Stitt headed powerfully beyond Munn from close-range.
Curtis and Scott combined moments later as the Light Blues looked to restore their two-goal advantage, but the latter dragged his finish wide of the target.
A slight nervousness began to creep into the Light Blues ranks as Luton poured resources forward in search of a leveller.
The introduction of Arran Kerr sparked a move to a three-man defence, which restored Rangers’ resilience and allowed the side to see out the victory.
RANGERS: Munn, Hutton, Wyllie, Campbell, Wark (Trialist, 83), Robertson (Scott, 63; Hynd, 84), Nsio, Burnside, Stewart (Kerr, 72), Curtis, Eadie
Subs not used: McGuire, Caldwell
LUTON TOWN: Coyne, Giwa (Roberts-Edema, 45), Fox, Martins, Paternoster, Massoko, Stitt (Trustram, 72), Lorentzen-Jones, Odegah, Xavier-Jones (Ioannides, 72), Phillips
Subs not used: Hockey, Chigozie