Ceri Holland flashed a header off target from Beata Olsson’s pitch across the box as Liverpool made a bright start to the second half.
But in a repeat of earlier in the game, the Blues followed up a disallowed goal with another that did count.
In the 53rd minute, a corner from the right flank was flicked in off Kerr, only for it to be ruled out.
There was no denying Kaneryd from the next wave, though, as she arced an excellent strike into the top corner from 20 yards.
The Reds were initially prevented from registering a consolation by a goalline clearance on the hour mark.
A deep corner kick found Lily Woodham and she hooked the ball back into the middle, where Gemma Evans’ header was on course for the net until Nusken got in the way.
Gareth Taylor’s side did score with 72 on the clock.
At a set-piece delivery from the other wing, Clark escaped her marker and sent a header over the line despite Nusken’s attempts to clear again.
Chelsea responded strongly and hit back with four more goals of their own in quick succession.
An unselfish Maika Hamano back-heel teed up Kaneryd, whose low drive deflected off Clark and beat Kirby.
Nusken powered in a header at the far post from Charles’ hoisted cross, before Kaneryd completed a hat-trick by nodding in a rebound when a Nusken effort bounced off the bar.
The away team increased their total to nine near the end as Bright made a one-two with Hamano and dispatched the ball emphatically.
Team
Liverpool: Kirby, Parry, Clark, Evans, Woodham (Bernabe, 76), Nagano, Maclean (Lundgaard, 46), Kapocs, Holland, Enderby, Olsson.
Unused subs: Laws, McDonald, Trueman.
