Kyle Walker-Peters drove towards the Arsenal box before whipping in a cross that clipped Gabriel and slipped underneath Bernd Leno on 24 minutes for the only goal of the game.
Saints had their chances to add to the lead with Danny Ings hitting the post with the rebounding coming off Leno and narrowly back into his own net.
Edward Nketiah had the best opportunity to draw Arsenal level after half-ftime, but Jan Bednarek took the sting out of the shot allowing Fraser Forster to toe the ball away to safety.
James Ward-Prowse did his defensive duties late to clear an attempt off the line 10 minutes from full-time to preserve the 1-0 lead.
The full-time whistle propelled Saints ahead in the competition, setting up a tie with Wolverhampton to be played on February 10 to be played at the Molineux Stadium.
Southampton (4-4-2): Forster; Bertrand, Stephens, Bednarek, Walker-Peters; Walcott, Diallo, Ward-Prowse, Armstrong; Adams (N’Lundulu 78), Ings (Long 85)
Unused subs: Lewis (GK), Valery, Vokins, Ramsay, Jankewitz, Watts, Chauke
Goals: Gabriel (OG 24)
Bookings: Stephens (56), Bertrand (84)
Arsenal (4-2-3-1): Leno; Cedric, Gabriel, Holding Bellerin (Lacazette 72); Xhaka, Elneny (Partey 58); Martinelli (Saka 58), Willian, Pepe; Nketiah
Unused subs: Luiz, Lacazette, Ryan, Chambers, Runarsson, Maitland-Niles, Willock, Saka