The Seagulls produced a competent display to extend their unbeaten away record to seven matches and leave Colchester five points behind second-placed Leeds.
Brighton defender Adam El-Abd had to clear from near his goal-line early on following Clive Platt's low cross.
But it was the Seagulls who looked more threatening and U's goalkeeper Ben Williams made a smart save at his near post to deny Alan Navarro, before the visitors claimed a penalty when Glenn Murray tangled with Magnus Okuonghae in the area.
Brighton keeper Peter Brezovan saved John-Joe O'Toole's hooked effort before Williams was called into action again just before half-time to save well from Inigo Calderon at his near post.
Colchester manager Aidy Boothroyd made a double substitution at half-time but Brighton continued to threaten, with Murray and Andrew Crofts both going close. However, neither team was able to break the deadlock and the spoils were shared.