It has also spared the club further embarrassment following two successive 1-0 home league defeats against Everton and Newcastle. However, despite a shaky start against Shakhtar, United dug in for the win that secured them top spot in Group A.
The pattern in the recent home Premier League defeats was that United largely dominated early on and created chances but a mixture of bad luck and poor finishing meant they were sunk by the attacking prowess of their opponents and they finished the games on the back foot.
In contrast, against the Ukrainian champions on Tuesday, United started sluggishly and had fewer chances but this time finished stronger although they had to thank the versatile Phil Jones who struck like a striker in the 66th minute with a well-taken goal.
Jones' volley ended a 309-minute wait for a goal at Old Trafford since Robin van Persie scored in the 1-0 victory against his former club Arsenal. That victory on 10th November was the club's last in the Premier League.
With United languishing in ninth place in the table, United's best chance of silverware this campaign could be the Champions League in which they have impressed, despite Moyes' lack of previous experience in the elite European competition.
United are unbeaten so far having won all their home matches and have conceded just three goals, fewer than any other team in the four completed groups.
Indeed the manager believes the team should now be expected to win.
I think we could be classed as one of the favourites," said Moyes. "We'll have to improve in order to progress. A club like Manchester United has to be trying to win the trophy."
The win has also affected the odds in the bwin football markets for Champions League bets.
The draw for the last 16 of the Champions League takes place in Switzerland on Monday and, having sealed top spot in Group A, the Red Devils will avoid most of the other big guns and cannot be drawn against another English side.