© PA Photos
Brighton had the majority of the chances in the first half, but a series of saves from Ben Hamer ensured that the sides finished the opening 45 minutes level.
The home side continued to look the stronger of the two teams at the start of the second half, as Vicente saw his cross stopped by Hamer.
The Brighton stopper was called into action again five minutes later, as he collected a dangerous cross from Johnnie Jackson.
Vicente also had a long-range effort in the second period, testing Hamer from 30 yards, but the Charlton keeper was able to tip the ball over the crossbar.
Both keepers made saves during stoppage time as the teams pushed for a late winner, but neither side were able to find the back of the net.
The result leaves Brighton sixth in the Championship table, while Charlton move up to 14th.