After suffering a 5-0 defeat against the same opposition in The Continental Cup at the weekend, Blues boss David Parker made five changes to his side, and they worked as they maintained their three point lead at the summit.
Goals from Karen Carney and Emily Westwood were enough to give the hosts the three points, an own goal from Hannah George proving to be the only breakthrough for Bristol.
FA WSL 1 League Table
Top three P Pts
Birmingham City 6 14
Chelsea 6 11
Liverpool 6 9
Second-placed Chelsea kept up the pressure on Birmingham in what is turning in to a pulsating title race with a win over Arsenal.
Japanese striker Yuki Ogimi and South Korean international Ji So-Yun grabbed the goals in the 2-1 victory.
Kelly Smith pulled a goal back from the spot for Arsenal – but Gilly Flaherty’s late red card ended their hopes of a comeback.
A Kate Longhurst effort secured the Merseyside bragging rights for reigning champions Liverpool as they defeated local rivals Everton.
Reds boss Matt Beard had claimed the match was a “must-win” in the build-up, and Longhurst’s finish after a lay-off from Natasha Dowie to claim the game’s only goal will have left him delighted.
Liverpool sit third in the league standings, five points adrift of Birmingham and two behind Chelsea.