Brighton started the strongest but fell behind after 28 minutes through Hakim Ziyech's low shot from the edge of the box. But the hosts grabbed a deserved equaliser on the hour mark when Webster met a corner by Alexis Mac Allister, who had moments earlier been denied by a full-stretch Kepa Arrizabalaga save.
Both sides went in search of a winner but substitute Neal Maupay was unable to turn in Tariq Lamptey's cross before Romelu Lukaku had a shot saved by Robert Sanchez. Chelsea stay in third place on 44 points, one point behind Liverpool and 12 adrift of Manchester City having played a match more than the leaders. Brighton extend their unbeaten run to five matches and are ninth with 29 points.