Albion had twice led through Stephane Sessegnon and Saido Berahino, but United avoided an embarrassing defeat as substitute Marouane Fellaini equalised with his first United goal before Blind scored the second leveller in the 87th minute to ensure Louis van Gaal’s side stretched their unbeaten run to three matches.
United’s erratic display was another reminder to van Gaal that his team remain very much a work in progress.
They are without an away league win this season, suggesting they are a long way from rivalling Manchester City and Chelsea for the title this term.
United sit sixth in the Premier League table – already 10 adrift of leaders Chelsea and just three ahead of the Baggies, who were excellent value for their point following a display which provided further evidence they are progressing under head coach Alan Irvine.
Albion began with the confidence of a side who had won two of their previous three league matches, with Sessegnon almost sending Berahino clean through with a threaded pass after five minutes.
And the home side had to wait just another three minutes to take the lead courtesy of a stunning strike from Sessegnon.
Van Gaal is unlikely to have been too impressed with Luke Shaw’s defending as the England left-back allowed Andre Wisdom to charge from his own half deep into United territory.
Wisdom’s clever cut-back was met with a wonderfully whipped first-time effort from the edge of the area from the former Sunderland man which flew inside the right upright.
– Lacking spark -United responded with a brilliant probing ball from Angel Di Maria finding Robin van Persie on the edge of the six-yard area, yet his first-time effort was blocked by Albion goalkeeper Boaz Myhill.
In the absence of the suspended Wayne Rooney, United lacked a spark in central areas with Juan Mata and Ander Herrera both not at their best.
Di Maria was more dynamic and the former Real Madrid midfielder forced a smart save from Myhill with a long-range effort.
Fellaini came on at half-time as van Gaal looked to spark his team into life.
It proved an inspired move as the Belgium midfielder required just three minutes to make an impact, controlling a Di Maria cross before bursting past Joleon Lescott and driving a rising shot beyond Myhill at his near post.
It left the Baggies’ media department red faced after minutes earlier their official account had tweeted: “Fellaini has now taken his tracksuit off, fortunately he has a Man Utd strip on underneath”.
The former Everton star, who has struggled for much of his time at United, looked poised to double the hosts’ misery as he bore down on a teasing cross from Adnan Januzaj, however Craig Dawson came to West Brom’s rescue with a last-ditch headed interception.
Having soaked up United’s pressure, the home side then left their opponents stunned with a clinical 66th-minute counter-attack which exposed the defensive frailties that have undermined van Gaal’s team since his pre-season arrival.
Chris Brunt’s threaded ball from midfield dissected the United rearguard far too easily and Berahino, played onside by Rafael, strolled through before calmly slotting inside the right post.
United almost levelled on 74 minutes when a Di Maria ball was headed back out by Lescott under pressure from Radamel Falcao, just on as a substitute, only for van Persie’s searing strike to cannon off the left post.
It looked set to be a night of frustration for the visitors, however Blind had other ideas as he curled a pinpoint shot inside Myhill’s near post from the edge of the area to spare United’s blushes.