Second-half goals from Morgan Amalfitano and Saido Berahino proved enough for the delirious Baggies despite Wayne Rooney netting for the fifth time in as many games.
Not even the introductions of Robin van Persie and Marouane Fellaini after the interval could swing the contest back in United's favour.
Fellaini did think he had equalised when he poked home Nani's low cross five minutes from time but the effort was ruled out for offside.
The result, at the start of what was supposed to be an easy run of fixtures, is a shattering blow to new manager David Moyes, whose team have now slipped six points off the pace in the early stages of the title race.
More importantly, United have now lost half their league matches and find themselves firmly in mid-table, with the faith the club's supporters vowed to have in their new boss already starting to fray judging by the boos that accompanied the final whistle.
There could hardly have been a greater contrast between the drab fare served up in the first-half and the 10-goal thriller between the sides that served as a fitting epitaph to Sir Alex Ferguson's managerial career in May.
Whereas the spectacular show at The Hawthorns had supporters on the edge of their seats, this soporific show had them slumped.
United were on top, as expected. But their efforts were sporadic.
Rooney, who retained the captain's armband, had one header saved by Boaz Myhill and sent another soaring over the bar.