After the restart, the Reds were grateful to captain Grace Fisk for a well-timed block that thwarted Madison Haley after she was teed up for a strike.
In response, Olsson could not keep a header down having found space and met a Holland corner kick to the near post.
Holland’s efficacy down the wing was evident again next as she hit the byline and flashed a cross into the middle that three teammates could not get contact on.
Liverpool substitute Aurélie Csillag might have made more of two free runs in behind. However, her first stumbled on a heavy touch and her second was foiled before she could pass to Holland.
As time ticked away, Fisk nodded wide with a headed effort from a corner kick, before the closest calls of the entire game for each side.
Brighton’s Manuela Vanegas was denied by a combination of Falk’s hand and the crossbar when she nodded at goal from yards out.
Then, Csillag was able to get in a low shot from the right of goal that Nnadozie got a touch on and deflected the ball narrowly wide of the opposite post.
From the resulting Holland corner kick, Martha Thomas’ header bounced off Fisk and was bound for the net until Maelys Mpome cleared off the line to ensure it ended goalless.
Team
Liverpool: Falk, Fisk, Clark, Bonner, Bernabe, Maclean, O’Sullivan, Kapocs (Csillag, 65), Enderby (Thomas, 65), Olsson, Holland.
Unused subs: Kirby, Evans, Woodham, Josendal, Bergstrom, Trueman.
Next up
The Reds are on the road in the WSL again next weekend, but with a much shorter trip to neighbours Everton.
Kick-off at Goodison Park on Saturday (March 28) will be 12pm GMT.