The Seagulls went ahead after 10 minutes when Orient goalkeeper Jamie Jones miscued his attempted clearance from a back-pass and gifted Glenn Murray the opening goal.
And they had a second goal disallowed when Murray again touched the ball home but was ruled offside.
Brighton had claims for a penalty turned away after Ben Chorley appeared to bring down Liam Dickinson, and Albion manager Gus Poyet was sent from the dugout by referee Steve Cook for his protestations.
Orient equalised through striker Scott McGleish after 53 minutes when an indirect free-kick was awarded in the area after goalkeeper Michel Kuipers was penalised.
A more even contest in the second half failed to produce many clear-cut chances, although Brighton midfielder Elliott Bennett had a fierce rising drive spectacularly tipped over by Jones as Brighton pressed.
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