Harry Redknapp's men were held for just the second time this season, but a point was enough to edge them back above Leicester City into top spot.
Richard Dunne had the best opportunity of the game for the hosts, seeing his header cleared off the line just after the hour mark.
However, neither side could get the breakthrough and Brighton lie 13th courtesy of their second 0-0 draw in four days.
The only goal of Wednesday's two Championship fixtures came at the Madejski Stadium as Reading left it very late to beat Leeds United 1-0.
With a goalless draw seemingly on the cards, Stephen Warnock was shown a second yellow card for a foul on Adam Le Fondre in the 96th minute.
The striker duly found the target from the resulting set-piece to record his fourth goal of the season and three points for Reading.
Brian McDermott, returning to his former club for the first time, saw his side slip to 11th as a result while Reading moved into seventh.
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