Stevie Campbell's side were under strength as the youth team got the rare privilege of playing at Ibrox.
The team lined up (4-4-2): Gibson - McMechan, McGrath, O'Byrne, Pope - Milligan, Mathieson, Ross McCord, Paterson - Feeney, Jeffrey.
But this was to be very much a backs to the walls afternoon.
From start to finish Rangers totally dominated, but the Tanandice youngsters defended brilliantly to keep the outcome in doubt until late in the game.
Apart from Tannadice keeper John Gibson denying John Fleck with his foot and Jordan McMillan heading over, Rangers struggled to get behind the United rearguard.
However, within two minutes of the re-start, only the crossbar saved United from going behind as Chris Smith powered a header from a Steve Lennon corner against the woodwork.
Yet four minutes later, home keeper Scott Gallacher was at full stretch to tip away Phil McGrath's header from a Neil McMechan free-kick.
But that only seemed give Rangers added impetus and Steve Lennon went through to lob Gibson, but sent the ball inches wide two minutes later.
Inevitably, the mounting pressure had to tell and did so midway through the second half. For once Rangers side found some space in the United box and the ball was laid back to Lennon who drilled the ball low in to the far corner from ten yards.
With fifteen minutes left, a lunging high tackle by John Fleck on Michael O'Byrne brought the offending Rangers player a straight red-card.
That gave United a wee chink of an opportunity, but, ironically, given how well they had defended, a mix-up in the visiting defence brought the ten-men a second goal.
Lennon nipped in between McGrath and Gibson to poke the ball home from just inside the box.
That ended any hopes of a United revival especially as a minute later, O'Byrne who had been off receiving treatment for a full three minutes after being fouled by Fleck, was sent off for a second caution.
Coach Stevie Campbell summed up proceedings, "Given all the circumstances, it was no disgrace to lose against a full strength Rangers team going for the title.
"Whilst we never got forward, we actually had the best chance when Phil McGrath almost scored early in the second half.
"But in the end, we couldn't complain at the outcome, though it was great experience for the lads to play at Ibrox."
Team: Gibson, McMechan, Pope, McGrath, O'Byrne, Mathieson, Milligan, Ross McCord (Allan 85), Feeney (McLeod 73), Jeffrey (Dow 78), Paterson. Subs not used: McKee, Prophy, Smith.