James Ward-Prowse's first goal of the season was enough for the Saints to win a game in which the Championship side held their own but struggled to create chances.
After ending an 11-month goal drought in Tuesday's defeat to Crystal Palace, Shane Long thought that he had scored again on 10 minutes when he rifled past David Button from a Steven Davis flick, only for the offside flag to deny him.
Ward-Prowse gave the hosts a warning with a 28th-minute shot which drifted a couple of yards wide of the post, and then opened the scoring soon after with an instinctive left-footed finish after the ball had richocheted to him inside the box.
Sofiane Boufal came close to doubling Southampton's lead within five minutes when he skilfully beat Ryan Fredericks on the left byline and squeezed a shot through Button's legs from a tight angle, but wide of the post.
Teenage sensation Ryan Sessegnon was Fulham's biggest attacking threat, and his free-kick delivery provided the Cottagers with their best chance of the first half as defender Tim Ream headed over the crossbar in stoppage time.
The Saints enjoyed a dominant 15-minute spell after the break and should have gone two up when Pierre-Emile Hojbjerg failed to lift his shot over Button from eight yards, after playing a neat one-two with Long.
Southampton goalkeeper Alex McCarthy was forced into his first save on the hour mark when Stefan Johansen shot from a tight angle, but only after Oliver Norwood had passed up a better shooting chance in the centre.
McCarthy's handling was less reliable on 77 minutes when he fumbled a cross from Norwood, only for Denis Odoi to blaze over the crossbar on the volley with what was Fulham's final chance to equalise and force a replay.
The Premier League visitors spurned several openings to secure the result, most notably when Jack Stephens headed against the woodwork from close range, and substitute Manolo Gabbiadini struck high from Mario Lemina's back-heel on 92 minutes.
Nevertheless, the Saints saw out the victory to give manager Mauricio Pellegrino a distraction from their poor league form.
FULHAM (4-3-3): Button; Fredericks, Kalas (Ojo, 66'), Ream, Odoi; Norwood, McDonald (Kebano, 56'), Johansen; PIazo, Fonte (Kamara, 76'), Sessegnon
SOUTHAMPTON (4-2-3-1): McCarthy; Bednarek, Stephens, Yoshida, Bertrand; Romeu, Hojbjerg (Lemina, 80'), Ward-Prowse, Davis, Boufal (Redmond, 70'); Long (Gabbiadini, 86')