Orient's hopes of picking up their first points of the season floundered from the moment captain John Mackie was sent off in the 15th minute.
Centre-half Mackie received a straight red card from referee Darren Drysdale when he under-hit a back-pass then compounded the mistake by pulling back Brighton striker Gary Hart.
The home side took just two minutes to make the extra man count. A corner by French winger Alexandre Frutos was cleared only as far as the edge of the area by the Orient defence and Paul Reid drilled in his second goal of the season.
The game was over as a contest by half-time. Adam El-Abd doubled Brighton's lead on the half hour when he cut inside before unleashing a left-foot shot from 25 yards.
Dean Cox added a third in first-half stoppage time with an angled drive in off the far post after he had been set up by Alex Revell.
The second half became a damage limitation exercise for Orient.
Captain Dean Hammond squandered the chance to stretch Brighton's lead further in the 61st minute when his penalty, awarded for a push on Reid by substitute Justin Miller, was saved by Glenn Morris.
Orient stuck gainfully to their task after the break and they managed to reduce the arrears after Reid cracked a free-kick from the edge of the area against the post.
Georges Santos dragged down substitute Jabo Ibehre inside the box and Matthew Lockwood scored from the spot for the second match in succession with seven minutes remaining.
Orient's fifth straight away defeat was completed in injury time when Doug Loft headed in a cross from fellow substitute Jake Robinson.