Saido Berahino looked to have secured all three points with his ice-cold finish until the Dutchman beat Boaz Myhill late on - though United's wait for an away win goes on
Stephane Sessegnon opened the scoring for the hosts early on, with Liverpool loanee Andre Wisdom racing down the flank and squaring for the Benin international, who fired a ferocious first-time shot past David De Gea and into the top corner.
|By Sam Lee at the Hawthorns
There will be plenty of these nights to come for Manchester United this season. The players certainly looked downbeat on their way off the pitch and Louis van Gaal was left to lament his men giving away two goals to the hosts, but at the same time it could easily be argued that the Red Devils got away with one.
West Brom again showed that United can be rattled by pace and tenacity and they also dug in deep when they had to. United needed three points here ahead of Sunday's clash with Chelsea, but once again it was defensive woes which cost them.
Unlikely goalscorers Marouane Fellaini and Daley Blind came up with the goods but only because Robin van Persie struggled without a partner in crime up front. Stephane Sessegnon and Saido Berahino, conversely, were clinical, and if these nights are to become common then a top-four finish is the absolute best United can hope for.
United's joy was short-lived, though, and the Baggies reclaimed the lead soon after via a bright counterattack, with Saido Berahino racing onto Chris Brunt's through-ball and nervelessly placing his shot beyond De Gea and into the bottom corner.
Robin van Persie smashed a shot against the foot of the post as United sought a response and they finally found a breakthrough when Blind stroked a loose ball into the bottom corner late on, though Van Gaal's men were denied the chance to record three back-to-back league wins for the first time since December 2013.
Radamel Falcao was left on the bench by the former Netherlands coach, who handed starts to the fit-again Phil Jones and Herrera in addition to Adnan Januzaj.
West Brom started the brighter and Sessegnon opened the scoring in the eighth minute with a superb first-time finish.
The Benin international met 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 full-back, who was included in the West Brom starting XI in place of Cristian Gamboa.
Van Persie was then denied by Boaz Myhill - in for the injured Ben Foster - at the other end as United sought an immediate response.
Di Maria also tested Myhill on two occasions but United, despite dominating possession for much of the first half, appeared to lack a cutting edge in the final third.
Fellaini was brought on for Herrera after the half-time interval and made an almost immediate impact by controlling a cross from Di Maria with his chest, before swivelling and unleashing an unstoppable drive beyond Myhill and into the top-right corner.
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 Brunt's incisive pass.
Van Persie struck the post with a vicious half-volley from the edge of the area before Di Maria was withdrawn for Ashley Young due to an injury to his right thigh.
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.