Chloe Peplow opened the scoring on 44 minutes for the title-chasing Seagulls with the second and clinching goal arriving in the 92nd minute from Amanda Nilden.
Back in action after a midweek WSL 2 game against Millwall was postponed, Spurs were put under pressure in the early exchanges as Ini Umotong threatened and Danni Buet fired wide.
Katie O'Leary was denied one-on-one as Spurs got into the game and then both teams hit the woodwork - Jenna Legg for Brighton before Bianca Baptiste hit the upright with Lucy Gillett beaten.
Buet, Lucy Somes and Aileen Whelan tried their luck for Brighton while at the other end, Gillet saved from Wendy Martin.