Danny Ings gave Southampton the lead in the 22nd minute off a cross from James Ward-Prowse and Ryan Bertrand made it 2-0 just before halftime with a powerful shot from a corner.
Ings’ goal was his fourth in as many Premier League games and his eighth of the season, the most of any Southampton player.
Norwich came back into the game in the second half, however, and cut the deficit through its top scorer Teemu Pukki in the 65th. Norwich could have claimed a point, but Sam Byram missed a good chance in the final minutes.
Southampton has now earned back-to-back Premier League wins for the first time since beating Tottenham and Brighton in March.
Meanwhile, Norwich is now four points adrift of safety. The Canaries have won just one of their last 10 Premier League games.
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