The Saints entered the match knowing that they needed to win to stand any chance of avoiding dropping down to the Championship for next season.
However, second-half goals from Carlos Vinicius and the returning Aleksandar Mitrovic secured all three points for Fulham, who have moved into ninth position in the table.
Southampton have spent the last 11 seasons in the Premier League, but they will be present in the second tier of English football for the 2023-24 campaign.
The Saints have now lost each of their last four in the league and are rooted to the bottom on 24 points, eight points behind 17th-placed Everton with two games left, meaning that their relegation has been confirmed ahead of their final two matches of the season against Brighton & Hove Albion and Liverpool.
The first half-chance of the match arrived in the 21st minute when Paul Onuachu took the ball away from Issa Diop before attempting to catch out Bernd Leno, but the Fulham goalkeeper was on hand to make the save.
Fulham wanted a penalty in the 25th minute for a handball on Lyanco, but the referee was not interested and VAR greed; Onuachu then flicked a throw in from Jan Bednarek into the arms of Leno, as the match started to open up after a cagey opening to proceedings at St Mary's.
Carlos Alcaraz tried his luck for the home side in the 33rd minute, but the attacker's effort was always rolling wide of Leno's post.
Fulham had easily the best chance of the first period, with Willian looking to have made the breakthrough in the 41st minute, but Lyanco did brilliantly to clear the Brazilian's effort off the line, and the two teams headed down the tunnel at 0-0 following a cagey opening 45 minutes.
Southampton had the ball in the back of the Fulham net through Alcaraz in the 47th minute, but the goal was disallowed for offside, and less than one minute later, the visitors made the breakthrough.
It was Vinicius with the goal, the forward tapping into an empty net after Harrison Reed had managed to steer the ball towards his teammate.
Fulham then doubled their advantage in the 72nd minute through Mitrovic, who headed a Harry Wilson cross into the back of the net to cap his return from an eight-game suspension.
As expected, Southampton committed a number of players forward in the latter stages in the hope of a comeback, with Kamaldeen Sulemana dragged one wide in the 84th minute.
However, there was to be no late response from the Saints, who will be playing Championship football during the 2023-24 campaign.