United eased past League One Shrewsbury with a professional and comfortable victory in Shropshire to set up an FA Cup quarter-final at home to West Ham next month.
This could have been a potential banana skin for the Reds and beleaguered boss Louis van Gaal but Shrewsbury never threatened United's dominance and goals from captain Chris Smalling, Juan Mata and Jesse Lingard proved a job well done for LVG's men.
Smalling went close with a header following a corner from centre-back partner Daley Blind, whilst Memphis, fresh from scoring in the Europa League on Thursday, had an effort tipped away by Shrews keeper Jason Leutwiler.
With United in total control of possession, it merely seemed like a case of when- and not if- we would open the scoring as the visitors continued to carve out the openings.
Mata had a deflected effort drop just wide, Memphis went close with a header and Anthony Martial then saw his shot blocked well by Leutwiler before the rebound was cleared off the line by Abu Ogogo.
Having had several chances but no go to show for their efforts, United were soon rewarded as the long threatened breakthrough finally arrived with two goals in quick succession.
First, Morgan Schneiderlin nodded down for Smalling to volley into the turf and over the keeper on 37 minutes, and then- in first half stoppage time- United doubled the lead.
Martial went down under a challenge on the edge of the area and Mata dispatched a perfectly-placed free-kick past the helpless Leutwiler and send the Reds in at the interval 2-0 ahead.
The match was already over as a contest, but the Reds made their last eight spot absolutely certain through Jesse Lingard's well-taken finish after a pin-point pass from Ander Herrera following a lovely counter-attack.
The young winger went close to a fourth and substitute Will Keane struck a post but then had to depart the field with a groin injury as United's injury jinx hit again.
Agogo might have claimed a consolation when was found in acres of space but headed wide when it seemed easier to score on 87 minutes, but the damage had long been done.
Sergio Romero's clean sheet remained intact and the Reds will now face West Ham at Old Trafford with a Wembley semi-final at stake.
Teenage Academy graduate Joe Riley became the latest United youth product to be handed a senior debut under van Gaal as he replaced Cameron Borthwick-Jackson for the second half.
Overall team performance: 7.5/10
United Faithful Man of the Match: Juan Mata