The Gunners boss Mikel Arteta named a second-string side, with only goalkeeper Bernd Leno, Cedric Soares, Rob Holding and Granit Xhaka remaining from the win over Newcastle United while the Saints were bolstered by the return of striker Danny Ings.
The hosts were creating the better chances in the early exchanges, as James Ward-Prowse hit the crossbar in the fourth minute with a swinging strike from a corner and Che Adams forced a save out of Leno ten minutes later after going through at the near post.
Southampton finally broke the deadlock in the 24th minute after defender Gabriel deflected Kyle Walker-Peters' low strike into the bottom corner.
Arteta's charges were probing after going a goal down but they lacked the creative spark in the final third, with shot-stopper Fraser Forster largely a spectator in goal and the Saints went to the break leading by an odd goal.
Ralph Hasenhuttl's troops had a good start in the second stanza as Ings came very close to doubling their lead five minutes from the break after going through on goal from a chip over the defence but his low strike came off the bottom post, ricocheted off the back of Leno and went wide.
Arsenal were a much improved side after they introduced Bukayo Saka and Thomas Partey on the hour-mark, as Eddie Nketiah had their best chance in the 67th minute after going through inside the box but his low shot clipped the foot of the diving Forster and missed just wide.
Despite bringing on striker Alexandre Lacazette in place of Hector Bellerin in the last 20 minutes, the Gunners were struggling to create clear chances, with the Saints kept their London counterparts at bay to book a spot in the fifth round.
