United, already crowned Premier League champions, looked set to mark Sir Alex Ferguson's last game in charge with an emphatic victory when they led 5-2 with 10 minutes to play, but the hosts hit back in stunning fashion to level it at five apiece.
And West Brom sprung another surprise on the title holders with a 2-1 triumph at Old Trafford in September but the trend since then has been one of declining fortunes for the Midlanders.
The subsequent 21 league games have yielded only two victories and the club have handed the reins to Pepe Mel in a bid to preserve their top-flight status.
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The visitors do not have any relegation issues with which to concern themselves but David Moyes's charges are in unfamiliar territory.
Since the advent of the Premier League in 1992, United have finished in the top three every season but they now sit seventh, well short of the division's leading sides.
It has been a campaign of inconsistency for the Old Trafford outfit, who have at times strung promising runs together - as evidenced by a six-match winning streak in all competitions during December - only to be let down by sporadic dips in form.
The last four league games have produced only five points, despite United enjoying a relatively kind run of fixtures that included matches against Stoke City, Fulham and Crystal Palace.
Hopes of achieving qualification for Europe now hinge on United securing a spot in the top five, although sixth is likely to be good enough after Manchester City's Capital One Cup success.
Moyes's old club, Everton, occupy sixth at present but have only a slender three-point advantage, with the two set to meet at Goodison Park on April 20.
United will have Juan Mata back after he was cup-tied for the Champions League clash against Olympiakos, but could be without Chicharito after the forward suffered a knee injury while on international duty with Mexico.
Midfielder Darren Fletcher had a happier midweek outing for his country as he marked his Scotland return with a second-half appearance in the victory over Poland.
West Brom, meanwhile, will not be able to call on striker Nicolas Anelka, who is under a club suspension as he awaits the final decision on how long his Football Association-sanctioned ban for his controversial 'quenelle' gesture will be.