The Holland international scored his first goal for the club to break Albion's hearts just as they looked like securing victory.
Saido Berahino had fired them 2-1 ahead with his seventh goal of the season in the second half after Marouane Fellaini bagged his first goal for United.
It had cancelled out Stephane Sessegnon's wonderful opener at The Hawthorns and the Baggies, who move up to 14th in the Barclays Premier League, were good value for a point.
The result means United boss Louis van Gaal has still not won away from Old Trafford with his side sixth in the table.
Ben Foster missed out for West Brom after suffering a calf injury in training and was replaced by Boaz Myhill in the Baggies goal.
Chris Brunt shrugged off a groin injury to start and Victor Anichebe was on the bench despite battling a hernia problem.
Andre Wisdom returned after being ineligible to face parent club Liverpool last time out meaning Cristian Gamboa dropped to the bench.
Adnan Janujaz made his first start of the season for United with Radamel Falcao left on the bench.
Phil Jones returned as Paddy McNair struggled with a hamstring problem along with fellow injury victim Antonio Valencia.
Michael Carrick, yet to make an appearance this season, made the bench as he stepped up his recovery from ankle ligament damage.
The changes, though, did little to end United's stuttering season as the Baggies grabbed a perfect start.
They had already dominated possession without hurting United before they swept ahead in the eighth minute.
Graham Dorrans flicked on Myhill's clearance for Wisdom to scamper down the right and his clever cut back found Sessegnon to finish emphatically into the top corner from 18 yards.
Myhill saved from Robin van Persie as United tried to find an instant response but the visitors were wasteful and their final ball was often too easy for the Baggies.
Myhill, who made a routine stop from Di Maria, was given catching practice as United toiled against organised Albion.
In contrast Berahino was giving Marcos Rojo an uncomfortable evening with the £16million defender constantly worried by the forward.
And the England Under-21 international was inches away from connecting with Dorrans' searching cross.
Myhill beat away Di Maria's drive on 31 minutes as United tried to up the tempo but they continued to be undone by their own wastefulness in the final third.
But they were almost handed a lifeline seven minutes before the break when Craig Dawson was forced to block Van Persie's shot after the striker robbed Joleon Lescott in the area.
It was the only time the Baggies had switched off and United were firmly on the back foot going into the second half.
Van Gaal reacted by replacing Ander Herrera with Fellaini and the midfielder made an instant impact on 47 minutes.
He collected Di Maria's hanging cross after out-muscling Lescott before thundering a right-footed effort high beyond Myhill from 15 yards.
It changed the complexion of the game with United pressing and Myhill saved Di Maria's tame effort.
But while the visitors were buoyant Albion held firm and regained the lead on 66 minutes.
It was another poor goal to concede from United as Rafael played Berahino onside as he broke onto Brunt's defence-splitting pass and coolly curled into the bottom corner.
United's rally began when Van Persie slammed an 18-yard volley onto the base of the post and Januzaj blazed the rebound over.
Rojo nodded well wide with nine minutes left but Blind secured a point with three minutes left when he bent the ball into the bottom corner from 18 yards after Rafael's cross was only half cleared.
Source : PA
Source: PA