To begin the second half, Fisk guided a header wide of the goal from a corner ball, while Erin Cuthbert saw a deflected shot fall the wrong side of the woodwork.
Chelsea again went close and had the ball in the back of the net on the hour mark via substitute Aggie Beever-Jones.
The striker rounded the defence in the box and tapped home into an empty net but was denied by a raised offside flag.
Moments later, she then lifted a lobbed effort over the onrushing Kirby towards goal, though the ball grazed the far post as she threatened once more.
Chelsea were dominating possession but it was Woodham who went closest with the game entering the final exchanges.
The full-back unleashed a shot from the edge of the box and saw the chance bounce just past the woodwork with goalkeeper Livia Peng urgently diving down quickly to reach the effort.
The Blues pushed on in search of a winner, though it was Ceri Holland who almost struck a winner in added time.
Her darting run down the right flank during a swift break was the last of the action as she cut into the edge of the penalty area, seeing her shot blocked with Liverpool relatively untroubled by the visitors in the final minutes.
Team
Liverpool: Kirby, Fisk, Clark, Evans, Woodham, Nagano, Kerr, Kapocs, Enderby, Olsson, Holland.
Unused subs: Laws, Borggrafe, Parry, Szymczak, Kiernan, Lundgaard, Maclean, Bonner, Silcock.
Next up
Liverpool turn their attention to the Women’s League Cup in their next outing against Sheffield United.
The Reds travel to Bramall Lane for a 6pm GMT kick-off next Saturday (November 22).
