Shakhtar started by far the brighter of the two sides, and their Taison-Alex Teixeira-Douglas Costa triumvirate in midfield would pose United problems all evening with their pace and thrust. Teixeira had the best chance of the opening period when his shot from an acute angle drifted just wide of the post as he worked some space away from Jonny Evans.
The Brazilian contingent for the visitors continued to look the biggest threat as Teixeira and Taison tore United apart again and again, with Douglas Costa also lashing a fine centre across goal which Adriano couldn't quite convert. Yet United had their moments too - Adnan Januzaj hit a fine effort with a turning snap-shot, but too close to Andriy Pyatov, before Wayne Rooney curled a free-kick around the wall but into the side netting.
Rio Ferdinand was perhaps a surprise inclusion in the squad tonight, and once again showed signs of his decline by allowing Teixeira and then Costa to get by him with remarkable ease. At the other end, United's best chance of an opener was looking like it would be from a Shakhtar mistake, and they were awarded one when Ashley Young took advantage of Darijo Srna's ball-watching, but with Rooney available for a simple square pass, the winger elected to loft it over the head of Pyatov, and the ball dropped wide of the open goal.
Young had another opportunity just after, being given a fine opportunity down the left channel after being picked out by Rooney, but he blazed a wild effort well off-target. United were looking pedestrian and very much second-best, and were continuing to be profligate on the rare opportunities they did have.
Shakhtar dropped off slightly in the second half, and Young again went close twice - firstly from a free-kick which Pyatov did well to keep out, and secondly as his attempted cross almost found the far corner of the net, but United were still looking for a goal having gone the last two games without scoring.
The introduction of Robin van Persie didn't provide United with as direct a threat as they might have liked, but he ended up having a hand in the opener anyway - his corner delivery was only half-cleared by the Shakhtar defence, and Phil Jones was able to spin and bury an effort low into the corner of the net and give United the lead.
The goal seemed to take the sting out of Shakhtar further, who could not replicate their energy and industry of the first half. The rest of the match petered out somewhat, although Van Persie did go close with a chip over Pyatov in the dying minutes.
In the end, United were able to claim the win. They were at the mercy of their opponents for almost the entire first half, but Shakhtar simply weren't clinical enough to get the goal and win the game. Instead, United kept their composure to score when it mattered. The old cliché is that to win while playing badly is the sign of a great team - that may not be the case here, but for David Moyes, it will do for now.