An own-goal from on-loan Eagles defender Matthew Upson gave Birmingham the lead before it was doubled by Dele Adebola on 59 minutes.
Dean Austin brought Palace back into the match with a goal on 61 minutes, but Trevor Francis' men proved good value for their three points.
A 33rd minute penalty from Lee Hughes kept West Brom in the race for the second spot behind Fulham and was enough to secure a 1-0 win at Norwich.
Crewe notched a valuable home win against Sheffield United with Kenny Lunt grabbing the only goal of the contest.
A 59th minute equaliser from Wayne Allison secured a point for Tranmere Rovers against Preston after a Jon Macken goal had given North End an early lead.
Huddersfield and Grimsby will both benefit from a 0-0 draw at the McAlpine stadium whilst the games between Gillingham and Wimbledon along with the clash between Stockport and Burnley were also goalless.
Wolves' home tie against Bolton was postponed due to Wanderers' involvement in the FA Cup on Wednesday.
For full match reports click below.
Crewe Alexandra 1 Sheffield Utd 0
Crystal Palace 1 Birmingham City 2
Huddersfield Town 0 Grimsby Town 0
