Leandro Trossard's fourth goal of the season gave the Seagulls all three points as well as their first away win of 2020, putting them nine points clear of the relegation zone with five games left.
Norwich drop their sixth game on the trot in all competitions and are seven points adrift at the bottom of the table with a third relegation in seven years almost certain.
Story of the game
Both teams made four changes to their starting lineup and it was the visitors who had the first chance as Aaron Mooy played in Aaron Connolly with a cross from the left, but his shot was off target.
The hosts had the majority of possession in the opening stages, but Onel Hernandez' 13th-minute effort blocked by Lewis Dunk represented their best effort.
The Cuban again had a sight of goal six minutes later after some neat buildup play. Ben Godfrey picked out Emi Buendia, who found Hernandez down the right, but he fired wide of Brighton's goal.
The Seagulls took the lead in the 25th minute as Timm Klose gave away possession in midfield to Mooy, who crossed for Trossard and he confidently swept the ball past Tim Krul at the far post.
Hernandez was Norwich's biggest threat and he continued to have chances, cutting in from the left and dragging his shot wide in the 33rd minute before Mooy blocked another effort in stoppage time.
Mooy continued to be influential in the Brighton attack and his free kick was met by Dan Burn who headed the wrong side of the post five minutes after halftime. Connolly saw his attempt blocked by Klose.
With the second half drinks break approaching, Josep Drmic hit one straight at Mat Ryan, who had little trouble gathering it in before Canaries manager Daniel Farke introduced Teemu Pukki and Todd Cantwell, his two leading scorers as part of a triple substitution.
Krul was called into action to save Yves Bissouma's lashed effort in the 69th minute and Norwich began to throw men forward in search of an equalizer. Their best chance came in the fourth minute of stoppage time as Adam Idah headed off the inside of the post.
Brighton saw out the remainder of the game and can now all but plan for a fourth successive season in the top flight while Norwich will begin preparing for life in the EFL Championship next season.
Daniel Farke's decision to leave Teemu Pukki and Todd Cantwell on the bench backfired
Norwich have scored just 25 goals in their 31 league matches this season with Pukki and Cantwell combining for 17 of them. The decision to name them as substitutes, despite the heavy fixture list, was puzzling to say the least. The Canaries had one shot on target in the match and by the time Farke brought them on, they didn't have enough time to make a genuine impact on the game.
Tariq Lamptey continues to impress
One of the shrewdest pieces of business Brighton manager Graham Potter did was to sign the 19-year old right back from Chelsea for £4 million. Making his third consecutive start, Lamptey excelled in all areas of the game. When defending, he played with control and patience. When attacking, he showed off his speed. As the Seagulls ready for the rest of this season and next year's top-flight campaign, expect to see the England U-20 defender play a prominent role.
Brighton's defense continues to shine
Despite the fact Norwich lacked the cutting edge in the final third to finish the many opportunities they had, Brighton still recorded their eighth clean sheet of the season and have surrendered just 44 goals this season, fourth in the Premier League. With Lewis Dunk and Adam Webster at the heart of the back four, Dan Burn flanked to their left and the emergence of Lamptey on the right, the Seagulls defense has a combination of youth, experience and composure to deal with any situation that will continue to serve them well moving forward.