Back at the Withdean Stadium after losing 3-2 in the Women's FA Cup last weekend, the ladies led Sunday's FA Women's Premier League encounter until a controversial late equaliser for the Seagulls.
Spurs dominated the first half. Wendy Martin just failed to convert Andra Marcoci's cross, Andra was then twice denied by Brighton goalkeeper Toni-Anne Wayne and struck the crossbar from a free-kick.
They deservedly took the lead on 29 minutes when Lucia Leon crossed from the right, Wendy rose high to beat Wayne to it, only to see her header strike the crossbar. However, she was alert to the rebound and nodded home from six yards.
Brighton came back into the game in the second half but Spurs remained a threat and Wendy came closest to adding to the scoresheet when she fired just wide from Maya Vio's pass. Shannon Maloney also had a decent effort that flew just off target.
The Seagulls levelled five minutes from time when Kirsty Barton - who hit the winner from a free-kick last weekend - stepped for another set-piece from the left angle.
This time, a low angled drive to the near post found its way home, only for the linesman's flag to go up for a possible infringement. However, after consultation, the referee awarded the goal and it ended all-square.
"We were disappointed," said manager, Karen Hills. "Even though that decision arguably went against us, we should have taken our earlier chances.
"On a positive note, I felt we dominated and played some excellent football. We'll look to build on that when we play Charlton on Sunday."
The ladies travel to Thamesmead to face Charlton in the FA Women's Premier League for a 2pm kick-off on Sunday.
They are currently ninth of 11 teams in the division, level on points with Charlton in seventh. Indeed, only three points separate Spurs in 11th and Portsmouth in fourth.