Wayne Gray fired Orient ahead before the break, but the Seagulls hit back with a second-half leveller from Nicky Forster and although Jason Demetriou restored the O's advantage, the impressive Dean Cox poached a second equaliser.
In a poor opening half it was Orient who took the lead with their first real effort on target.
A neat move saw Adam Boyd and Sean Thornton combine and Thornton's well-weighted through ball found Gray, who raced clear and crashed the ball past keeper Michels Kuipers for his third league goal of the season.
Orient started to apply the pressure as Charlie Daniels and Paul Terry both went close, but Brighton always looked dangerous and George O'Callaghan fired just over the bar.
On the stroke of half-time the visitors almost levelled through skipper Dean Hammond but his header was ruled out for a push.
Orient almost extended their lead at the start of the second half when Jason Demetriou shot over and then Daniels was denied by a smart stop from keeper Kuipers.
But Brighton stormed back and after Alton Thelwell blocked O'Callaghan's effort the visitors equalised on 68 minutes.
Adam Chambers and Daniels got into a tangle and Forster cashed in when he smashed in an effort from 25 yards which flew through Stuart Nelson's grasp.
Orient responded two minutes later when substitute John Melligan crossed from the right and Demetriou turned and fired into the roof of the net.
But Brighton hit back and five minutes later Cox netted from close range after Forster's header came back off the bar.
Both sides had chances to win the game late on as substitute Jake Robinson clipped the bar and Hammond headed an effort wide, while deep in stoppage time Kuipers saved superbly to deny Gray.