Tom Adeyemi missed a great chance for City after nine minutes when he found himself with space inside the box, but the midfielder could only send his effort over the crossbar.
Michael Tonge ruffled a few feathers when he barraged his way towards the box before unleashing an effort from distance, however, the ball just evaded the City goal as it flew wide of the right post.
Ross McCormack produced some good work just before half time when he fed Tonge, however, the midfielder saw his effort saved by Butland at the bottom corner.
City's hopes of staying in the league took a blow in the 58th minute when Matt Smith headed home from the centre of the box into the bottom right corner, having latched onto Tonge's cross.
Smith turned provider minutes later when Leeds grabbed their second goal, as he provided a neat headed pass, which left Danny Pugh with the chance to angle a shot across the goal and into the opposite corner.
Birmingham's nightmare afternoon was confirmed 12 minutes from time when Paul Caddis put the ball into his own net.