Ross Stewart's ice-cool penalty in stoppage-time at Craven Cottage sealed Southampton's fifth-round upset.
It was an embarrassing loss for Fulham manager Marco Silva, who paid the price for a selection gamble that backfired.
Silva made nine changes to following a disappointing 1-0 defeat against West Ham in the Premier League earlier this week, but his switches failed to produce the desired result.
Southampton won it in the first minute of stoppage-time when Finn Azaz was fouled by Fulham defender Joachim Andersen and Stewart drilled his spot-kick past Benjamin Lecomte.
Relegated from the Premier League last season, they are through to the FA Cup quarter-finals for the first time since 2022.
Southampton's success served as a fitting tribute to the greatest day in the club's history.
Their players wore a yellow commemorative kit to mark 50 years since they wore the same shirts when Bobby Stokes sealed then second-tier Southampton's shock 1976 FA Cup final win against Manchester United at Wembley.
Southampton's current crop still have a way to go to emulate the achievement of Lawrie McMenemy's men.
But Tonda Eckert's side are unbeaten in 10 games in all competitions as they chase FA Cup glory and a place in the Championship play-offs.
Later on Sunday, Sunderland travel to Port Vale, who sit bottom of League One, and Leeds host second-tier Norwich, while West Ham meet Brentford on Monday.
Arsenal, Chelsea, Manchester City and Liverpool have already booked their places in the quarter-finals.
