Louis van Gaal's side were heading towards a third defeat in eight Premier League games when the in-form Saido Berahino put West Brom 2-1 up with 24 minutes remaining at The Hawthorns.
However, holding midfielder Blind then emulated Marouane Fellaini by scoring his first goal for United, denying the hosts a notable victory.
West Brom took an early lead through a fine goal from Stephane Sessegnon in a game that provided further evidence of United's defensive fragility.
Fellaini equalised in stunning fashion within three minutes of his introduction at the start of the second half, but Alan Irvine's men moved back ahead against the run of play when Berahino broke clear to grab his sixth league goal of the campaign.
The Benin international met Andre Wisdom's low ball with a curling effort into David de Gea's top left-hand corner, following an excellent run down the right from the on-loan Liverpool full-back, who was included in the West Brom starting XI in place of Cristian Gamboa.
United appeared more likely to grab a second goal thereafter, but were caught short at the back again as Berahino restored Albion's lead.
The England Under-21 international is behind only Manchester City's Sergio Aguero and Chelsea's Diego Costa in the Premier League goalscoring charts and displayed his quality once again, capping an excellent West Brom move with a confident strike into the bottom-right corner from Chris Brunt's incisive pass.
With United's most creative player on the sidelines, West Brom looked set to hold on.
However, there was to be a late final twist as Blind picked the perfect time to open his account and salvage a point, although the nature of United's performance is unlikely to put an end to questions over the Old Trafford club's ability to sustain a title challenge.
