Ward-Prowse was the beneficiary of a gratuitous bounce as the ball fell kindly to him in a 1-0 finish.
Alex McCarthy made his third consecutive start in goal and had little to do, but kept out Stefan Johansen after the break.
The win marks the first in all competitions for Southampton since November 26 when they beat Everton.
The tie was void of any action throughout the first half until Ward-Prowse dug the ball from out of his feet before curling his shot wide of the far post on 28 minutes.
Two minutes later, however, the midfielder was wheeling away in celebration having given Southampton a 1-0 lead.
Boufal tried to thread a pass through the box, which bounced off Shane Long and a Fulham defender before finding Ward-Prowse who swept the ball into the corner.
McCarthy would make a comfortable save from a tight angle on Johansen on the hour mark whilst Southampton failed to further their lead.
Jack Stephens thumped the underside of the crossbar from Ward-Prowse’s corner, but a second goal wasn’t need as Southampton progressed in the competition.
Fulham: Button, Fredericks, Kalas (Ojo 67), Ream, Odoi, McDonald (Kebano 56), Norwood, Johansen, Piazon, R. Sessegnon, Fonte (Kamara 74).Unused subs: Norman (GK), Djalo, S. Sessegnon, de la Torre, Ojo.
Bookings: McDonald (50).
Southampton: McCarthy, Bertrand, Yoshida, Stephens, Bednarek, Davis, Romeu, Højbjerg (Højbjerg 79), Boufal (Redmond 70), Ward-Prowse, Long (Gabbiadini 86).
Unused subs: Forster (GK), Targett, Tadic, Sims.
Goals: Ward-Prowse (30).
Bookings: Bednarek (73).