Danny Welbeck had opened the scoring for the Red Devils but a second-half equaliser denied the Scot his second Champions League victory in as many games
Ryan Giggs made history by breaking the Uefa Champions League appearance record after coming on to replace Marouane Fellaini.
But Danny Welbeck was the initial hero as he gave United the lead in the 18th minute before Taison equalised with 14 minutes remaining - but the game was more notable for Giggs' landmark appearance.
|By Tom J Doyle
David Moyes may be a little disappointed his side could not hold onto all three points at the Donbass Arena but, all in all, a 1-1 draw with Shakhtar Donetsk is a good point for Manchester United considering their early season travails.
Nemanja Vidic was in imperious form at the back, while goalscorer Danny Welbeck was sharp and the likes of Rafael and Tom Cleverley showed that United's youth is still in rude health. The hosts continually threatened without creating too many chances, though they fully deserved Taison's emphatic equaliser. One suspects both managers will not be too unhappy tonight.
Shakhtar coach Mircea Lucescu made two changes from Saturday's 2-2 draw with Metalurh Donetsk, Olexandr Kucher and Luiz Adriano coming in for Sergey Krivtsov and Facundo Ferreyra.
Lucescu had stated before the game that he felt David Moyes was struggling because he had not yet found his best starting XI and, again, the United manager made wholesale changes from the home defeat against West Brom at the weekend.
Only goalkeeper David de Gea and Michael Carrick kept their place from Saturday, with Wayne Rooney missing out altogether with a shin injury picked up in training the day before.
After a quiet opening, Robin van Persie had the first sight of goal in the eighth minute, bringing down Tom Cleverley's pass before firing high and wide from 20 yards.
There was little further goalmouth action until the visitors took the lead in the 18th minute when Fellaini drove to the byline before cutting the ball back in search of Welbeck.
Yaroslav Rakitskiy was in position to intercept a pass but the defender slipped as he stuck out a leg, allowing the ball to run for Welbeck to sweep beyond Andriy Pyatov from six yards.
The home side were struggling to create anything going forward and did not manage an effort on target until the 39th minute when Alex Teixeira's weak shot from the edge of the box was straight at De Gea.
The second half followed a similar pattern to that of the first, Rakitskiy's wayward free-kick from 35 yards in the 50th minute representing Shakhtar's only notable effort of the opening exchanges.
Van Persie had a rare sight of goal in the 71st minute, turning on the ball inside the area before seeing his low effort blocked by the covering Rakitskiy.
But five minutes later, the hosts equalised out of nothing.
Rakitskiy broke down the left and although Nemanja Vidic intercepted his cut back, the ball fell perfectly for Taison to smash the ball beyond De Gea from 10 yards.
And Taison then came close to a winner five minutes from time as his deflected drive was tipped over brilliantly by the alert De Gea at his near post.
The result sees both teams move to four points from two games in Group A, although Moyes may be disappointed that his side could not see out a game in which they held the lead.