Salomon Rondon scored the winner for West Brom putting a dent on United's top-four challenge.
Rondon controlled Sebastien Pocognoli's cross from the left before burying the ball into the left corner on 67 minutes against an increasingly toothless United, who had lost Mata to a second yellow card on 26 minutes.
The Spain international was booked for not retreating and blocking a quickly-taken free kick before receiving his marching orders two minutes later for kicking Darren Fletcher's shin in a clumsy tackle.
United are three points behind Manchester City in fourth, while West Brom climbed to 11th with a third win in four league games.