Wanderers stayed on course for a possible trip to Wembley as a belated goal-rush swept them into the quarter-finals of the Papa Johns Trophy.
The Whites had to wait to ensure their passage through after spurning a handful of chances to make it an early night.
But two goals within the space of eight minutes just passed the half-way point of the second half finally allowed Wanderers’ superiority to count.
Dapo Afolayan notched his sixth goal of the season and victory was then all but assured when Morley claimed his first goal since August with a clinically despatched free-kick.
The margin could have been wider as Ian Evatt’s men out-played a young United line-up with a slick performance.
And two more goals in stoppage time via a deflected Amadou Bakayoko effort and Conor Bradley's close-range finish ultimately gave the scoreline a more realistic look as Wanderers booked a last-eight date in January with a potential trip to the Wembley final now just two more wins away.
As expected, Wanderers made their intentions clear with a powerful line-up which also offered the chance of a return to action for the first time in close to two months for Will Aimson.
The defender slotted back in smoothly in the continued absence of captain Ricardo Santos and made his presence felt at both ends of the pitch in a first half that somehow finished goalless.
Aimson steered one effort wide at full stretch and as well as having the ball in the net for an effort disallowed after touching an offside Dion Charles on the line also delivered a superb long ball for Charles which the striker couldn’t steer past stranded keeper Nathan Bishop.
Bradley and Afolayan both had efforts blocked in front of goal as free-flowing Wanderers made chances at will.
And Bishop made one fine save to keep out a Gethin Jones’ strike after the stand-in skipper had run onto Elias Kachunga’s perfectly weighted pass shortly before making way for Eoin Toal after picking up a knock.
Wanderers should have taken firmer control of the tie although United’s youngsters – backed by a vocal band of travelling fans – could have pinched the lead themselves.
James Trafford made his first appearance in the competition this season and the on-loan Manchester City keeper had to make an excellent block to deny Shola Shoretire from United's best move of the night before palming away a header from Noam Emeran.
Nearly all the attacking play came from Wanderers, though, and two minutes into the second half they again had the chance to go in front.
This time Afolayan fed Charles but his finish was awry and the frontman was off target again shortly afterwards when he didn’t get enough of a head on a sumptuous cross from Kieran Sadlier.
United’s goal continued to lead a perilous life and after Kachunga intercepted an attempted pass out from Bishop, Afolayan clipped the ball over the bar as he got ever closer.
With half an hour to go, Evatt made three further changes to try and finally break the deadlock and five minutes later the opening goal did come.
One of the substitutes, Bakayoko, was involved although it took a mis-cued header from United full-back Marc Jurado to present Afolayan with the chance he coolly took after nipping in ahead of Bishop to round the keeper and slot the ball home and add to his goal against Barrow in the last round.
The ever-dangerous Afolayan was then inches away from curling an effort into the top corner following another pleasing move as Wanderers looked to make absolutely sure.
And with a quarter of an hour to go it was job done as Morley showed his class with a clever free-kick which deceived Bishop to curl straight into the keeper’s near top corner from a tight angle to cap another outstanding evening's work from the Wanderers' midfielder.
Afolayan was denied a second by Bishop’s late save but there was still time for two more late goals as the scoreline belatedly gave a truer reflection of Wanderers’ progress through.
United substitute Sonny Aljofree turned in a Bakayoko shot from in front of goal and then when Afolayan again wriggled free to pick out Bradley at the far post, the on-loan Liverpool youngster tapped in to sign off on a high as Wanderers reached the quarter-finals for the first time.
Wanderers: Trafford; Jones (Toal 39), Aimson (Johnston 63), Iredale; Bradley, Lee (Sheehan 63), Morley, Sadlier; Kachunga (Williams 78); Charles (Bakayoko 63), Afolayan. Substitutes: Dixon, Beck.
Booked: Iredale
Manchester Utd U21s: Bishop; Jurado, Bernard (Aljofree 88), Hardley, Murray; Iqbal; Hansen-Aaroen (Collier 69), Shoretire, Savage, Emeran; Hugill (McNeill 68). Substitutes: Mastny, Kambwala, Oyedele, Norkett.
Booked: Bernard, Murray
Referee: Martin Coy
Attendance: 4,735 (visitors 1,615)