The Seagulls struggled in an opening draw against Bristol Rovers and they laboured in front of their own fans again against Leyton Orient.
The visitors had the better of the game on a sweltering afternoon on the south coast and, with sharper finishing, would have taken all three points.
Brighton failed to get going in a dismal first-half display.
They were grateful to Michels Kuipers for keeping them on level terms at the break. The long-serving Dutch goalkeeper dived to hold a curling effort from the lively Jason Demetriou and then stuck out a hand to divert the same player's low cross, with Adam Chambers poised for a simple tap-in.
Brighton boss Micky Adams made a double substitution at half-time, bringing on the fit-again Kevin McLeod and Jake Robinson on the wings for David Livermore and Dean Cox.
McLeod injected a bit more life and tempo to the home team's attacking thrusts. The former Colchester wide man had a half-volley held at his near post by Glenn Morris and the Orient keeper again came to his side's rescue two minutes from time.
He foiled McLeod's shot with a superb one-handed stop after a smart turn and cross from Glenn Murray.
Adam Virgo also had a header from McLeod's corner scrambled off the line but Orient, spearheaded by the elusive Adam Boyd, still looked more likely to break the stalemate.
Demetriou slotted wide after Boyd's shot on the turn was charged down amid claims for handball.
Kuipers then came smartly off his line to smother Demetriou's effort at the end of a neat Orient build-up.