Having pushed Rangers so hard in their recent Youth Cup semi-final, this was by contrast a disappointing performance by the Tannadice teenagers.
In a game of relatively few chances, the Ibrox side posed the greater threat, scoring twenty minutes into each half.
Yet, it was United who had the first chance Sean Fleming heading just over after ten minutes.
Ten minutes later Rangers went ahead, Ica Bagci netting the rebound from ten-yards after a William McLachlan drive came back off the post.
Again at the start of the second half, United went close, Johnny Russell just failing to hit the target from a Fraser Milligan cross.
And they were made to pay for that miss when Rangers added a second on 65 minutes, Andrew Shinie slotting home after John Gibson could only parry a John Fleck strike.
Dundee United: Gibson, Milligan, McGrath, Fleming, Paterson, Ryan McCord, Ross McCord (Kenny Smith 80), Anderson, Love (Elfverson 70), Russell. Subs not used: Burns, Brophy, Mathieson, Colgan, Lee.