It was a cathartic release for the Scotland international, whose first Achilles injury with Sunderland in 2023 occurred in a cup game at Craven Cottage.
Fulham twice had the ball in the net but saw their opening goals ruled out by the officials, as they failed to beat the Championship challengers.
But Saints were deserving winners against Premier League opposition, with a plethora of nearly moments and missed chances throughout the day.
It extends play-off chasing Southampton’s unbeaten run to an impressive 10 games in all competitions, with eight wins and two draws in that time.
Head coach Tonda Eckert was repaid for naming a near-full strength side for the cup game, despite a vital league trip to West Brom days later.
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Jack Stephens and Shea Charles were not in the squad at all and given a full rest by Eckert, while Stewart returned after his absence last week.
Saints made four changes, with Nathan Wood, Flynn Downes, Caspar Jander and Tom Fellows in for Stephens, Cam Bragg, Charles and Kuryu Matsuki.
Marco Silva made nine changes to his Fulham team that were beaten by West Ham midweek, though it still represented a Premier League-level XI.
Former Saints midfielder Harrison Reed was among those who came in, while there was still space for the likes of £27million forward Oscar Bobb.
The Putney End was packed with 4,800 Saints fans who made the short trip up to West London, and chances were almost free-flowing at that end.
Cyle Larin and Finn Azaz both missed early cutback opportunities – the latter stopped by top defending – while Saints threw bodies in front of shots.
Ryan Manning then inadvertently blocked a quickly taken Daniel Peretz goal kick, with the ball falling to Rodrigo Muniz to smash into the open goal.
But the referee’s whistle had already gone as the box was still crowded with players, sparing Saints a comical concession inside the first 20 minutes.
With almost the next passage of play, Scienza burst through on goal two-on-one with Larin to his right, but his solo effort squaked just wide of the post.
Bobb clipped the frame of the goal from a tight angle for the Cottagers, who were piling men forward and leaving spaces for Eckert’s side to explore.
Saints continued to threaten on the counter-attack but lacked the final touch to finish a move, as the even teams went into the break level at 0-0.
Muniz headed over the bar shortly after the restart, and Timothy Castagne had a rebound goal ruled out with Joachim Andersen’s initial effort offside.
Tom Fellows tamely hit goalkeeper Benjamin Lecomte with a chance inside the box, just as Fulham were starting to impose themselves as favourites.
Lecomte then had to get to full stretch to tip a deflected Azaz shot onto the bar, while Peretz denied Ryan Sessegnon with his face in the closing stages.
It was inside added time when Matsuki intercepted a goal kick, Stewart played through to Azaz and the Irishman was tripped by Andersen.
The referee pointed straight to the spot, and Scotland hopeful Stewart stepped up to power into his left corner and send the away end bezerk.
It secures Saints a place in the last eight of the competition, in their 50th anniversary year of winning the trophy as a second division team.
Fulham: Lecomte; Castagne, Andersen, Cuenca, Sessegnon; Cairney (Iwobi, 64), Reed (Jimenez, 90), Chukwueze, Smith Rowe (King, 88), Bobb; Muniz.
Unused subs: Leno, Tete, Bassey, Berge, Lukic, Robinson.
Booked: Cuenca, Chukwueze.
Saints: Peretz; Bree, Harwood-Bellis, Wood, Manning; Downes, Jander (Bragg, 70), Fellows (Matsuki, 82), Azaz, Scienza (Edozie, 82); Larin (Stewart, 70).
Unused subs: Long, Quarshie, Jelert, Romeu, Archer.
Booked: Downes, Matsuki, Azaz.
Referee: Jarred Gillet.