The Saints supporters were finally able to relax in the seventh minute of stoppage time when Sam Gallagher scored his side's fourth to confirm the win.
Below, Sports Mole takes a closer look at the key talking points from the game.
On target: 6
On target: 3
Was the result fair?
Southampton definitely deserved to collect all three points. A 4-2 defeat suggests that Norwich were closer to claiming something that they didn't actually deserve. Southampton should have never been under so much pressure in the closing stages after dominating for the majority of the contest.
It will be a strange team talk for Saints manager Mauricio Pochettino. Southampton were brilliant for two 20-minute spells in each half, but they never really hit fifth gear for an extended period. They appeared relaxed in possession for most of the match and were far superior to their opponents. However, two big mistakes at the back almost prevented them from climbing to eighth in the Premier League.
The club's supporters won't be fooled by the scoreline if they watched the game. On a day when Norwich really needed to produce their best, they were very poor. They struggled to compete for the ball in midfield and were second best to everything. Two late goals increased hopes in the away end, but Norwich were only really in the game for 10 minutes.
Sports Mole's man of the match
Gaston Ramirez: It wasn't an easy decision today, but the award goes to a player who was only on the pitch for an hour. Ramirez has struggled to produce his best since joining the club in 2012, but today was certainly one of his better performances. A clever pass to Schneiderlin for the opening goal was a highlight and his all-round display was very promising before he limped off with a hamstring problem.
Chris Hughton is guilty of committing the biggest error today. Norwich were clearly struggling to threaten the Saints defence as they persisted with playing in front of the home back four. Instead of changing things at half time, Hughton delayed making a substitution until the after the visitors had conceded a second goal. It was a performance which was crying out for Nathan Redmond's pace, but the Canaries manager waited too long to make a change.
Kevin Friend had a good game in the middle as the contest passed by without any controversial moments.
Southampton: Pochettino takes his side to the capital to face Tottenham Hotspur next Sunday.
Norwich: The Canaries face Sunderland in a crucial game at Carrow Road in seven days.