كتب : Hatem Maher
An own goal by Birmingham keeper Maik Taylor early in the first half gave United the lead before Welsh winger Ryan Giggs doubled added the second.
United striker Wayne Rooney sealed the victory seven minutes before the final whistle.
The result put the Red Devils in second place of the Premiership table with 66 points and one game in hand, 12 points behind leaders Chelsea.
United needed only three minutes to grab the lead when Taylor failed to block Giggs' tremendous free kick into the top right hand corner only to put it into his own net.
The welsh international maintained the lead 13 minutes later as he slotted home from close-range after being set-up by Rooney.
The misery of Birmingham, who suffered a humiliating 7-0 loss at the hands of Liverpool in the FA Cup recently, continued as England international Rooney added the third in the 83rd minute after he met Cristiano Ronaldo's header with a cool finish past Taylor.
In other matches, Middlesbrough beat Bolton 4-3 and Charlton Athletic defeated Newcastle United 3-1.