The away side dominated for large parts of the opening half, but West Brom hit back level before the break. New signing Shane Long cut inside Chris Smalling before shooting low underneath the body of De Gea in the Manchester United goal.
Goal scoring chances were few and far between after the restart but with nine minutes remaining United claimed the winner. Summer signing from Aston Villa Ashley Young drilled in a cross which was deflected into the net by West Brom full-back Nicky Shorey.
Next up for United is a home fixture against Tottenham Hotspur on Monday, August 22, while West Brom travel to Chelsea on Satuday, August 20.