Both sides were playing their final fixture of 2024, and each manager looked reasonably happy at full-time.
A draw suits both, especially Brighton who will finish the year behind only the big four of Chelsea, Manchester City, Arsenal and Manchester United.
Their success this year has been built around their home form. Dario Vidosic's side remain unbeaten in front of their own fans this season with four wins and two draws.
That record was in danger against Tottenham and had to be saved late on by an unlikely hero.
Left-back Olislagers, who joined Brighton from Twente this summer, was in the right place at the right time but still needed a moment of magic to score her first goal for the club.
The 24-year-old's shot was perfect. Hit with power from a tight angle her volley dipped into the far corner to earn her side a point.
It meant Brighton also ended their rather embarrassing two-match losing run when hosting Tottenham, having lost 8-0 and 3-1 at home to Spurs over the past two seasons.