Stephens, who was celebrating his 24th birthday, also celebrated his first goal for the club after just four minutes he poked in from a chaotic free-kick from close-range.
Cedric came close to making it the perfect start, but the defender narrowly missed on converting Shane Long’s cross with nine minutes gone.
With Watford adapting to life without Marco Silva as boss, Richarlison tried to test Alex McCarthy from distance on the stroke of half-time. The goalkeeper, however, was equal to the attempt.
Long was a constant thorn in the Hornets defence and twice threatened before the hour mark whilst Pierre Emile Hojbjerg struck the bar from 25 yards out.
Watford limped to their ninth defeat in 13 at the full-time whistle, which led to Silva’s dismissal whilst Southampton progressed unconvincingly into the next round of the competition.
Southampton: McCarthy, Bertrand (Pied 40), Hoedt, Cedric, Romeu, Hojbjerg, Davis, Tadic (Carrillo 83), Boufal (Yoshida 67), Long.
Unused subs: Forster (GK), Lemina, Ward-Prowse, Gabbiadini.
Goals: Stephens (4).
Bookings: Cedric (63).
Watford: Karnezis, Kabasele, Janmaat, Mariappa, Holebas, Doucoure, Capoue (Okaka 47), Carrillo (Pereya 57), Richarlison, Watson, Gray.
Unused subs: Bachmann (GK) Pereyra, Prodl, Zeegelaar, Sinclair, Success.
Bookings: Watson (61).