Danny Welbeck gave United the lead in the 18th as he slid in between two players to finish off Marouane Felliani's low cross, but Shakhtar leveled in the 76th from Taison's volley after Nemanja Vidic failed to clear a cross.
Both teams have four points in the group.
Cristiano Ronaldo continued his sparkling form in the Champions League with two goals in Real Madrid's 4-0 victory over FC Copenhagen.
Ronaldo scored with two headers, first meeting Marcelo's long cross in the 24th minute and then capping a creative buildup in the 65th.
He scored a hat trick in Madrid's opening 6-1 win over Galatasaray two weeks ago.
Angel Di Maria made up for several first-half misses against Copenhagen by scoring Madrid's third goal, in the 71st minute, before scoring again in stoppage time.
Madrid, under pressure following a poor domestic run and without the injured Gareth Bale, completely dominated the Danish champions at the Santiago Bernabeu Stadium and now leads Group B with six points.
Juventus had a 2-2 against Galatasaray in the other group match today and is in second spot with two points.
- AP