The Reds took a first-half lead through Leah Galton's left-footed strike from six yards out, and doubled their lead in the 80th minute thanks to a tap-in from Ella Toone, Hannah Blundell assisting both goals.
With three wins from the opening four games, Marc Skinner's team now sit fourth in the WSL table, level on points with third-placed Chelsea and three behind North London duo Arsenal and Tottenham Hotspur.
FIRST HALF
United dominated first half proceedings, controlling possession, creating several chances and receiving little threat back from Birmingham City.
The search for an opening goal ended thanks to an incisive run from left-back Hannah Blundell.