Katie Zelem opened the scoring for the Reds after a minute but reigning champions Chelsea roared back with goals from Karen Carney, Kirby, Drew Spence and Eniola Aluko putting them 4-1 up at half-time.
Caroline Weir and Emma Lundh reduced the deficit for Liverpool early in the second half but Kirby and Spence added further goals to make it four wins from four games for the second-placed Blues, who are now three points behind leaders Manchester City.
Elsewhere, Emily Westwood scored the only goal as Birmingham won 1-0 away at Notts County to move up to fourth.
The defender headed home Jo Potter's free-kick on 69 minutes to move Birmingham level on points with third-placed Arsenal.
Source : PA
Source: PA