A scrappy goal by Che Adams and Oriol Romeu's sizzling strike secured the win on a night where the hosts were utterly dominant.
Ralph Hasenhuttl's men had a total of 27 shots in the match and could have had many more goals - Mohamed Elyounoussi going close on three occasions in the match.
The Canaries have the inspired Angus Gunn to thank for it being a respectable scoreline, with the former Southampton man also making good saves to deny Kyle Walker-Peters and Stuart Armstrong.
A flurry of opportunities for Armstrong and Walker-Peters prompted Sky Sports pundit Jamie Carragher to label the clash 'men against boys.'
The result sees Saints move up to ninth in the Premier League table while Dean Smith's side remain bottom.
Norwich had the first chance of the game when Teemu Pukki wove his way into the box before finding Josh Sargent and after his blocked shot fell to Billy Gilmour, the Scot struck the ball well but it rebounded out for a corner.
Southampton came close to taking the lead when Armando Broja created space in the area then took a shot but it was well saved by Gunn.
Gunn had to make a low save to deny Mohamed Elyounoussi from close range after the ball was flicked on to him by Broja from a James Ward-Prowse cross.
Southampton were eventually rewarded for their possession and dominance in the 36th minute.
Valentino Livramento made a promising run down the right and crossed the ball into the box, before a goalmouth scramble ensued.
The ball rebounded goalwards off Max Aarons, but Gunn was able to parry the ball straight into the path of Adams, who missed his first shot before putting the ball over the line from the floor.
Saints started the second half in the way they finished the first, with two well-struck corners that Norwich were only just able to keep away from the home side's forwards.
Gunn also had to come off his line to head the ball ahead of Broja, who was almost picked out expertly by a long-range Ward-Prowse cross.
Stuart Armstrong managed to test Gunn from outside the area, but his well-struck shot was straight at the goalkeeper.
As the barrage of Southampton chances continued, Kyle Walker-Peters also hit a volley goalwards, but Gunn was alert once again.
Southampton eventually doubled their lead when Romeu hit a powerful volley from the edge of the box straight past Gunn for his first Saints goal since October 2020.