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Andrew Shinnie looked to get the home side on the board early on, attempting a 16-yard shot inside the opening minute, but his finish was too high.
It looked like Birmingham would break the deadlock in the 10th minute when Jesse Lingard was brought down by Alan Dunne, but David Forde was able to keep the on-loan Manchester United youngster's spot kick out.
The hosts continued to see the majority of the possession, and were able to take the lead 19 minutes in, when Shinnie curled in a free kick for Muprhy to tap in from close range.
Chris Burke had a chance to double Birmingham's lead, but his effort was well saved by Forde. Murphy was able to add his second of the clash moments later, beating the Millwall keeper with a free kick.
Jimmy Abdou tried to pull one back for the Lions, but his attempt from close range went high.