Brighton showed attacking intent from the start managing four goal attempts in the first five minutes.
The home side replied with shots from Paul McVeigh and Iwan Roberts that were safely gathered by Michele Kuipers.
After 17 minutes Robert Green did well to get behind a long-range shot from Steve Sidwell and was tested again in the 35th minute by a shot from Graham Barrett.
There was little Green could do however when Steve Sidwell smashed home a half volley when Simon Rodger's left-wing corner deceived the Norwich defence.
Rodger was replaced by Charlie Oatway following an injury on the stroke of half time and the sub got in the first shot of the second half.
Brighton keeper Kuipers was booked for dissent four minutes into the second period and two minutes later Clint Easton made way for David Nielsen making his 50th appearance for Norwich.
There followed sustained pressure on the Brighton goal, during which Mark Rivers put the ball in the net, but the effort was ruled offside.
Nathan Jones was booked for a foul after 63 minutes and then injury caused Darren Kenton to be substituted by Ian Henderson.
Nigel Worthington made his final substitution 13 minutes form time sending on Zema Abbey for Roberts.
Rivers was again unlucky when he beat Kuipers only to see his shot bounce back off the crossbar.
Late on Phil Mulryne's header was blocked by the Brighton keeper and there were several scrambles in the visitors' goalmouth, before the large contingent of travelling fans could celebrate a rare away victory.