David Moyes' men got back to winning ways after successive home league defeats thanks to Phil Jones' 67th-minute effort and the hard-earned triumph should boost confidence ahead of the weekend trip to Aston Villa.
The Ukrainians were confident in possession and a frustrating first half unfolded with Ashley Young spurning the Reds' best two openings. The left-winger did well to beat Darijo Srna to a Ryan Giggs chip but then lofted a lob inches off target before flashing off target when put clear by Wayne Rooney.
Adnan Januzaj turned to fire straight at Andriy Pyatov and Rooney went close with a free-kick that brushed the netting but Shakhtar had chances of their own and looked a real threat. Alex Teixeira clipped wide of the far post after being released by Taison and ran through again unchecked to work David De Gea. Teixeira also robbed Rio Ferdinand, only for the defender to block Fred's effort from the cross.
There was a fright at the start of the second half when a corner was allowed to run to Yaroslav Rakitskiy and his shot deflected off Jones and clipped a post. United responded with a Shinji Kagawa effort and a measured chip over the bar by Rooney but the goal only arrived after the introduction of Robin van Persie and Tom Cleverley.
Van Persie's corner fell to Jones and the midfielder executed a controlled volley past Pyatov to break the deadlock and earn the acclaim of the Old Trafford faithful. Srna fizzed in a left-footed strike that De Gea held