The Red Devils avoided suffering a third straight defeat on home soil for the first time since 1962 courtesy of a solitary strike from Phil Jones - much to the relief of manager David Moyes and an expectant fan base.
It was a far from a vintage display by the reigning Premier League champions, as they struggled at times during a nervous first half which saw Ashley Young lob one effort narrowly wide and badly slice another, but they will avoid the big boys in the last-16 of European competition and that is job done for now.
Jones' match-winning goal arrived on 67 minutes, with the versatile England international crashing home a volley from 12 yards out after the Ukrainian visitors had failed to deal with a Robin van Persie corner.
Defeat on English soil spells the end of the road for Shakhtar, who finish third in Group A and will have to make do with the consolation prize of a place in the Europa League.
Whilst Moyes said in the build-up he took complete responsibility for United's downturn in fortunes, his players have been the ones out on the pitch.
As has often been said, they won the Premier League by 11 points last season, so their collective ability should be enough to shoulder some of the burden themselves.
When Jones surged onto Rafael's return pass and brought a close-range save out of Andriy Pyatov it did seem United were in the mood to at least maintain their impressive European form.
Pretty soon though, the anxiety that has enveloped them during those back-to-back home losses to Everton and Newcastle United returned.
Taison's through-ball presented Alex Teixeira with a clear run at goal and his flick rolled narrowly wide of the far post.
Though Adnan Januzaj did bring a decent save out of Pyatov, it was the start of an extended period of Shakhtar pressure, in which United, clearly lacking in confidence, struggled to string more than a couple of passes together.
A lone cry of "get a midfield in there" could be heard about the general groans and not even Wayne Rooney curling a free-kick into the side-netting could counter the growing feeling United were in perilous danger of falling behind.
Fred should have turned that fear into reality after Teixeira had robbed Rio Ferdinand but despite the ball being rolled invitingly into his path, the shot lacked power and did not threaten the home goal.
A couple of good opportunities for Young came and went.
The winger lobbed Pyatov with the first but as the ball dropped narrowly wide, Young would have known if he had elected to square for Rooney, the United skipper would have had a tap-in.
Young also drove wide after collecting Jones' crossfield pass, adding to the growing sense of frustration.
Rafael blocked a Vyacheslav Shevchuk effort at the start of the second-half before the Shakhtar midfielder saw another attempt flick off the outside of a post after taking a slight deflection off Jones.
In response, Ryan Giggs meekly fired at goal following decent approach play by Young and Shinji Kagawa. Young's long-range curling effort to the far post dropped narrowly wide and Rooney's ambitious chip brushed the roof of the Shakhtar net.
Van Persie's introduction brought added potency to the home attack and the Dutchman was a key figure in breaking the deadlock, albeit by taking the corner Jones lashed home.
The relief that rippled round the stadium as Jones' volley hit the net was palpable and whilst Shakhtar did try to respond, they were the ones who lacked conviction as Bayer Leverkusen's win away to Real Sociedad dumped them out of Europe's premier club competition.