Alex McCarthy inexplicably gifted Arsenal the opening goal when he passed the ball directly to Nketiah, who was easily able to dispatch into an empty net.
It was an uphill battle for Southampton until halftime when a double substitution was made.
The introduction of Kyle Walker-Peters and Shane Long breathed life into the hosts with Nathan Redmond and Long each coming closes to an equaliser.
Redmond hit the side netting on 73 minutes after James Ward-Prowse’s cross found its way to the winger.
Long drew a big save from Javi Martinez four minutes later with the goalkeeper pouncing on the loose ball ahead of a charging Danny Ings.
Willock then doubled Arsenal’s lead after he scored off the rebound from a free-kick, which saw Jack Stephens receive a straight red card for bringing down Pierre-Emerick Aubameyang as the last man.
Southampton: McCarthy, Bertrand, Bednarek, Stephens, Valery (Walker-Peters 46), Hojbjerg (Vestergaard 90+1), Ward-Prowse, Armstrong, Redmond, Ings (Romeu 90+1), Obafemi (Long 46)
Unused subs: Gunn (GK), Vestergaard, Danso, Romeu, Vokins, Smallbone, Tella, Adams
Bookings: Stephens (RED 85)
Arsenal: Martinez, Tierney (Kolasinac 70), Holding, Mustafi, Bellerin, Saka, Xhaka, Ceballos (Maitland-Niles 80), Aubameyang, Pepe (Wllock 64), Nketiah (Lacazette 79)
Unused subs: Macey (GK) Papastathopoulos, Smith, Nelson, Ozil
Goals: Nketiah (20), WIllock (87)
Bookings: Mustafi (11), Saka (48)