The Canaries failed to win away from Carrow Road as they were relegated from the Premiership last season but the victory over Brighton followed three points at near neighbours Ipswich when they were last on their travels.
Nigel Worthington's side were without injured strikers Dean Ashton, Leon MacKenzie and Peter Thorne for the visit to the South Coast, but they still had too much firepower for struggling Brighton.
Darren Huckerby launched their third victory out of four in the 22nd minute when a pass from Moroccan international midfield Youssef Safri beat Brighton's offside trap.
It left Huckerby in the clear and he calmly bent a right-foot shot in off the far post.
Dean Hammond, guilty of a glaring miss for Brighton in their 0-0 draw at Leciester on Tuesday, should have equalised in the 36th minute when he fired over from eight yards.
It proved to be a costly miss, Paul McVeigh doubling Norwich's lead in the 41st minute.
Brighton left-back Kerry Mayo allowed Dean Marney to get in behind him from Calum Davenport's free-kick. The on-loan Spurs midfielder squared for McVeigh to slot his first goal for 14 months from close range.
Brighton manager Mark McGhee made three substitutions in the space of four minutes early in the second half in a bid to get back into the game.
One of the replacements, French left winger Alexandre Frutos brought the Seagulls back into contention in the 68th minute with an unstoppable shot from the edge of the area.
With Brighton pressing forward in search of an equaliser, substitute Ian Henderson sealed their fate with five minutes left.
Henderson, on for the injured Safri for the second half, latched on to a pass from McVeigh and rounded Paul Reid before curling in a shot from just inside the Brighton box.