Southampton could be about to climb into the top six of the Championship if they manage to hold onto a slender lead at St Mary's.
Norwich started the match brightly and had the best of the opening stages. After a couple of weak efforts on goal, Anis Ben Slimane forced Daniel Peretz into action with a fierce shot, which the Saints keeper did well to parry wide.
Paris Maghoma should have been booked for four late challenges in the early stages, the worst of which was on Samuel Edozie in the first five minutes.
Edozie had a good shout for a penalty waved away when he was bundled over inside the box as he waited for a Finn Azaz cross to come down out of the night sky.
Edozie had the ball in the back of the net in the 23rd minute, only for the goal to be ruled out for an offside decision against Finn Azaz.
The Republic of Ireland International made up for the offside a minute later when he showed more desire than the Norwich defenders to nick the ball through before finishing high into the left corner of the net.
A long throw-in by James Bree was flicked on by Cyle Larin into an innocuous area on the edge of the box. Finn Azaz had no right to win the ball with two Norwich defenders in good positions to clear the ball.
Ruairi McConville was particularly weak in the challenge and pulled out as Azaz put his foot in bravely before firing past the onrushing Vladan Kovacevic in the Norwich goal.
Southampton 1-0 Norwich
Edozie forced Jack Stacey into a late challenge with 10 minutes left of the opening period as the winger marauded down the left wing. Referee Lewis Smith had little option but to book the Norwich City right-back.
A wayward effort from Maghoma sailed high and wide of the Southampton goal and into the Northam stand as the fourth official signalled for two minutes of additional time at the end of the first half.