The Reds secured their second win in the league phase thanks to Natalia Ramos' 93rd-minute decider.
Marie Höbinger (two) and Neve McDonald were also on the scoresheet for the visitors.
See the story of Wednesday night's game in the video above.
Subway Players Cup highlights: Birmingham City 3-4 Liverpool
Watch extended highlights of Liverpool FC Women's 4-3 victory at Birmingham City in the Subway Players Cup.
