Wanderers had taken a first-half lead after Seagulls winger David Lopez put through his own net, but four second-half minutes saw Brighton score three times to leave Dougie Freedman's men still without a win this season.
Jay Spearing put through his own goal in the 53rd minute, before Inigo Calderon and Will Buckley both found the net to stretch the Amex club's unbeaten run to six matches.
Wanderers have only collected a single point on the road this season and have been severely lacking in creativity since Chris Eagles hobbled off with an ankle injury against Burnley on the opening day of the season.
But the former Manchester United man, who bounced back with a goal against Derby on his first full 90 minutes of the season on Tuesday night, did add some early spark and potency to a team deprived of confidence.
David Ngog failed to keep his cool when one-on-one with keeper Tomasz Kuszczak, who made a save down low to deny the French striker after a mix-up in the Brighton defence.
Bolton, however, continued to pose a threat and took the lead in bizarre fashion on 29 minutes when Lopez steered an innocuous corner by Eagles into his own net.
Kazenga LuaLua hit the bar with a stinging, rising 25-yard drive and Ashley Barnes almost converted a teasing Buckley cross as Brighton went close to an immediate response.
Oscar Garcia's men, who went into the match on the back of consecutive 0-0 stalemates against Reading and QPR, were struggling to initiate the fluid, high-tempo passing game that they have become renowned for at the Amex Stadium.
They did, however, demonstrate the kind of second-half resilience that has helped them go unbeaten since the second weekend of the Championship season, and they were level within eight minutes of the restart.
Spearing brought down Stephen Ward on the edge of the box and LuaLua's resulting free-kick was headed into his own net by the former Liverpool midfielder.
Calderon then produced an exquisite half-volley from the edge of the area three minutes later to put the home side ahead after a pull-back by Buckley, who then completed Brighton's victory in the 57th minute.
The roving winger cut inside from the right and hit a curling left-foot shot past keeper Adam Bogdan as a shell-shocked Bolton continued to fall apart.
Brighton went close to increasing their lead with Bogdan denying Buckley from close range and LuaLua sending a long-range effort wide.
Substitute Jermaine Beckford should have provided a consolation goal for the away side, but he failed to keep his composure after being set-up by defender Marc Tierney.