The young Gers raced out to an early advantage when Ashton Patton added his third goal in as many games to Corey Ngwenya's opener.
Luca Rankin then restored his side's two-goal cushion later in the first-half, before Conor Owen got in on the act early in the second half to add a fourth of the evening.
However, the Ayrshire side put up a fight when they struck twice in quick succession, setting up a final stanza where Rangers had to show their defensive resilience.
And they duly did so to see out a crucial victory as attention now turns to next week's KDM Evolution Trophy clash against Peterhead.
There was a raft of changes from the side which squared off against Queen of the South in KDM Evolution Trophy action ten days ago, with 2008-born Cameron Fernie the oldest member of the squad.
Rangers set out their intentions early as Coben Fergusson, fresh from scoring his first Scotland Under-17s goal, showed tremendous persistence to win a free-kick on the edge of the penalty area.
From the subsequent delivery, a James Reid header was denied by the crossbar, likewise Ruaridh Hall on the follow-up, but on the third attempt Ngwenya reacted first to plant beyond the Killie goalkeeper from close-range and break the deadlock.
The visitors were still reeling from the concession of the opener when the Gers struck again three minutes later.
The move was initially brought to life by a wonderful spin from Hall who quickly moved possession onto Calum Young. The full-back lifted his head advanced on the right, picking out a gorgeous delivery towards Patton who directed his header into the far corner.
It was a third strike as many games for the 17-year-old who is enjoying a purple patch in front of goal.
Killie mustered a response when Cole Burke guided a lovely outside-of-the-boot pass into Noah Simpson, who couldn’t generate the required purchase to test Rydnn McGuire.
Soon after, they reduced the arrears when the lively Burke burst through on goal and, with only McGuire to beat, slid his finish under the goalkeeper.
However, the action continued apace in Milngavie, and the Gers restored their two-goal advantage when Rankin collected possession in midfield and advanced into space.
Suddenly, an opportunity from distance presented itself, with the midfielder arrowing a crisp low effort into the bottom corner and out of the reach of the Killie goalkeeper.
McGuire, recently involved with Scotland Under-19s, kept the scoreline as it was with a fantastic reflex stop, while he gratefully watched another effort flashed across his goal ricochet off the post before the interval.
The Gers had their tails up to open the second period as Owen went close from a corner when he peeled into space at the far post and had not only one but two efforts thwarted by the goalkeeper.
And the away side failed to heed the warning as, from the resulting corner, Rangers added a fourth of the evening.
Again, the Gers showed their set-piece prowess in winning the first contact, and when Reid headed back into a congested six-yard area it was Owen who was on hand to lash into the bottom corner on his unfavoured left side.
Such was the frenetic nature of the contest that the Ayrshire outfit were offered a route back into the contest just two minutes later when Simpson went over inside the penalty area, a spot-kick was awarded, and Ruari Ellis slotted home from 12 yards out.
Three minutes later, Killie struck for a third time to make it a contest.
The hosts failed to clear their lines defensively as Adam Law danced across the byline before squaring the ball into the path of Cole Bickerton, who couldn’t miss from close-range.
Suddenly, the momentum of the contest had shifted, and it was incumbent on a young Gers side to regain their composure.
Daniel Owoyomi, summoned from the bench, almost turned home from another corner when Rankin's delivery dipped dangerously into the vicinity of the near post.
Burke then flashed over the top from distance as the final quarter of an hour loomed into view.
A rasping effort from Hall forced the Killie goalkeeper into a low save, while a Gers wall stood tall from a free-kick with just three minutes to play.
And the young side held out amid spurts of the visiting pressure to secure a priceless three points.
RANGERS: McGuire, Young (Caldwell, 70), Reid, Owen, Ngwenya (Ramage, 84), Patton, Rankin, Hutton, Fernie (Owoyomi, 65), Fergusson, Hall
Subs not used: Millarvie, Johnston, Morris, Molloy
KILMARNOCK: Morrison, Davis, Spence, Leddy, McMurray, Ellis, Burke, Foster, Simpson, Bickerton, Law
Subs: Redford, Sweeney, Frew, Feeney, Peacock, Obaisuwa