
The final score was 2-0 in favor of Birmingham.
Wrexham is four points behind the sixth-placed Hull after the defeat.
Carlos Vicente and Christoph Klarer scored the goals for Birmingham.

Wrexham's playoff hopes took a hit after a 2-0 loss to Birmingham, leaving them four points behind the playoff places with four games remaining. Birmingham's Carlos Vicente and Christoph Klarer scored to secure the victory, while Wrexham failed to register a shot on target.
Wrexham missed the chance to move within a point of the Sky Bet Championship playoff places after they suffered a 2-0 defeat by Birmingham at St Andrewâs.
The Red Dragonsâ dream of an unprecedented fourth straight promotion was dealt a massive blow after they were beaten for a second straight match which leaves them four points behind sixth-placed Hull with four games to play.
A string of first-half saves from Arthur Okonkwo stopped Birmingham from having a deserved lead at the break but there was nothing he could do at the start of the second period to stop Carlos Vicente from nodding in his third goal for the club since joining in January.
Chris Daviesâ side had lost three in a row coming into the contest but oozed confidence in front of a full house which was capped by Christoph Klarer stabbing in a second to seal the points.
Wrexham were toothless in attack and failed to register a shot on James Beadleâs goal. Beadle was simply a bystander in a dominant Birmingham performance which helped lift them up to 15th in the table.
With Wrexham chasing the playoffs, Birmingham may have expected a much stiffer contest but instead cruised their to a first win in over a month. The hosts started on the front foot and forced Okonkwo into a couple of early saves to deny a pair of headers from Ibrahim Osman and August Priske albeit in comfortable fashion.

Christoph Klarer wraps up Birminghamâs win with the second goal. Photograph: Ryan Browne/Shutterstock
Birmingham continued to be dominant but were unable to find a way past Okonkwo who had to react quickly to stop Vicente from poking the home side in front. Wrexham had yet to make their mark in the attacking third and had been limited to just a couple of efforts from range courtesy of Oliver Rathbone and Callum Doyle.
Wrexham just about managed to settle but had to rely on Okonkwo for a fifth time in the contest to stop Vicente from one-on-one range following a long and hopeful ball up the field to keep it goalless at half-time.
But, the Blues finally had their reward with the opener three minutes after the break. Kai Wagner sent a delivery into the area and Vicente jumped highest at the far post to head home. Birmingham were still in the ascendancy in search of a second, some neat link-up play between Priske and Jay Stansfield ended with the latter aiming high above the crossbar.
Phil Parkinson brought on Josh Windass and Nathan Broadhead in an attempt to get something clicking up the top end of the pitch for Wrexham who had produced very little with a quarter of the game to go.
Birmingham were relentless and doubled their lead in the 71st minute. An in-swinging corner from Paik Seung-Ho found Klarer at the far post who muscled Max Cleworth out the way and stabbed in from close range which was enough to wrap up a much-needed Blues win.
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