The home side made a promising start to the game but they fell behind midway through the first half.
World Cup winner Shinobo Ohno’s corner was nodded down by Leah Williamson to former England captain Casey Stoney, who fired home from close range to claim her sixth goal of the season.
Jordan Nobbs, who scored a spectacular long distance effort in the 4-0 win at Manchester City last weekend, almost made it two with another strike from range which was tipped over by Rebecca Spencer.
Birmingham thought they had a penalty on 49 minutes when Jade Moore was brought down but referee Amy Fearn reversed her original decision and awarded a corner.
The visitors doubled their lead on 70 minutes when Ohno crossed for Freda Ayisi to slot the ball home.
Carney pulled a goal back for Birmingham after converting a penalty following Alex Scott’s handball, but Birmingham were unable to snare an equaliser in the game’s closing stages
The result leaves Birmingham a point behind Liverpool Ladies and three behind leaders Chelsea, but David Parker’s side have a game in hand on their title rivals.