Caroline Weir scored twice and Natasha Harding was also on target at Keepmoat Stadium as Liverpool moved above Birmingham, who beat the Reds last time out.
Victory at home to Arsenal in their final game of the season on November 6 will see Liverpool finish behind champions Manchester City and runners-up Chelsea in the standings.
The Belles had taken the lead through Rhiannon Roberts, but Scotland international Weir curled in to equalise before striking superbly from distance to make it 2-1, and Harding curled a third in from the edge of the area.
