Leeds took a 13th-minute lead through Amanda Barr, but within 60 seconds Becky Hall equalised and then Steph Samuels put the Blues in front six minutes before the break.
With the clock showing five minutes of first-half stoppage time, however, Sue Smith levelled.
And a close match was won by Steph Houghton in the 69th minute, the midfielder scoring with a nicely placed 20-yard free-kick.