Csillag was introduced after the break in response to the opening goal by head coach Taylor.
Her first involvement was to see a penalty claim waved away, while her second on the hour led to parity restored with Liverpool on the attack.
It was a clever bit of play from the Reds to unlock the Tottenham defence, as Kapocs played a ball to Fuka Nagano on the right wing.
The midfielder's delivery swung into the area and Csillag sprinted across and in front of her marker to greet the ball with a well-timed header to score.
Following the goal, Liverpool pushed on in search of the lead as they dominated possession.
Vivien Endemann saw another penalty appeal for the Reds turned down, while Ramos had a driven shot saved by Lize Kop.
Csillag then shot over following a delivery from substitute Alice Bergstrom, before the winger herself produced a dazzling run into the box only for Kop's push over the bar deny her a goal.
At the other end, Olivia Holdt forced Keating into a strong save to her left following a curling effort in a rare Tottenham advance.
Liverpool almost won it late on, as Marie Höbinger slid Csillag into the area, though Kop was out quickly to block her effort as she attempted to round the goalkeeper.
**Team**
**Liverpool:** Keating, Kerr, Clark, Fisk, Bernabe, Nagano, Ramos, Endemann (Bergstrom, 78), Holland (Höbinger, 65), Kapocs, Olsson, (Csillag, 46).
**Unused subs:** Laws, Roman H., Enderby, Woodham, Agrez, Trueman.
**Next up**
The Reds visit Manchester City for matchday three of the new Barclays Women's Super League season on Friday (September 18).
Kick-off at Joie Stadium is 7pm BST. [**View ticket details here**](https://www.liverpoolfc.com/tickets/match/manchester-city-women-v-liverpool-fc-women-womens-super-league-2026-27).