Sussex started the day on 326-4, still trailing by 41 runs, but Brown's 113 helped them to 527 all out.
England all-rounder Jordan (4-32) then struck twice early on with the ball as Gloucestershire collapsed to 26-3.
Jack Taylor made an unbeaten 52, but two more wickets from Jordan and Danny Briggs left the visitors at 149-8 at stumps, still trailing by 11 runs.
Gloucestershire have only one wicket left in hand, as Liam Norwell is unable to bat after suffering a concussion.
Ben Brown's century and four wickets from Chris Jordan helped put Sussex on the verge of beating Gloucestershire.