Leading for almost an hour following Danny Welbeck's well-taken opener, United looked set for victory until Taison capitalised on a rare error in the visitors' defence to earn the hosts a share of the spoils.
Still, it made United the first English team to take a point off the Ukraine heavyweights, after previous failures in the Donbass Arena for Arsenal (twice), Tottenham and, last season, Chelsea.
And after a shocking sequence of results in the Premier League, the breathing space will come in handy for the Red Devils ahead of Saturday's trip to Sunderland.
"There was a bit of disappointment we didn't see the game out," said Moyes.
"But Shakhtar are a good team, with a great reputation, so I don't think it was too bad a result.
"We never play for a draw we play to win. But the players knew it was going to be a tough game and we defended very well for the majority of it.
"It wasn't the most exciting game, both teams had three points before the match and I think we both wanted to make sure we got something from the game."
The result was even more impressive considering United were without Wayne Rooney, who suffered a shin injury in training yesterday.
Rooney's absence immediately sparked fears the 27-year-old might miss England's vital World Cup qualifiers against Montenegro on October 11 and Poland four days later, upon which Roy Hodgson's hopes of reaching next summer's Finals in Brazil now hinge.
Source: PA
Source: PA