Jerome Osei, who came on as a substitute just minutes earlier, stepped up from 12-yards, however his effort from the spot was just over the bar.
In the final 10 minutes, Dean Benamar had Palace’s best chance of adding a third with an effort that just glanced across the face of goal.
The referee’s whistle brought an end to proceedings after five minutes of added time, capping off a successful afternoon on the south coast for the young Eagles.
The result means the side are up to eighth in the U18 Premier League South, level on points with Brighton, Chelsea and West Ham United.
**Brighton:** Mansell (GK), Hayden, Anah (Cullinane, 61), Mthunzi (Silsby, HT), Vickery, Mackley (Outen, 82), West, Nti, Belmont, Gorman (Ibrahim, 61), Oriola.
Sub not used: Ferdinand.
**Palace:** Hill (GK), King, Benamar, Adams-Collman, Somade, Walker-Smith (Fasida, 60), Whyte, Danaher, Casey (Drakes-Thomas, 63), Williams (Okoli, 60), Henry (Osei, 74).
Sub not used: Mason (GK).