Jonas Olsson scored the winner eight minutes after the restart when he headed home from close range.
Egyptian striker Mido was included in the starting lineup after recovering from a hamstring injury that ruled him out of the midweek Carling Cup defeat to Manchester United.
His compatriot, midfielder Mohamed Shawky, also took part but he was replaced by Frenchman Didier Digard on the hour mark.
Mido made quite an impact but he couldn’t score against a determined West Brom side.
He played a neat give-and-go with Brazilian striker Afonso Alves after 18 minutes. The latter went clear on goal but his fierce drive cannoned off the bar.
Boro piled on pressure after falling behind but failed in their attempts to restore parity.
Their best chance came in the 65th minute when Stewart Downing crossed from the left to Mido, whose effort was blocked by keeper Scott Carson from point-blank range.
Alves tried to notch home on the rebound but his shot went just wide of the post.
Mido, who repeatedly protested against the referee’s decision, was booked in the 58th minute for remonstration.