Grzegorz Rasiak opened the scoring when he capitalised on Romain Larrieu's error to coolly slot in.
Arygle pressed and Marcel Seip nodded over before Hayles headed wide.
He made amends with a leveller into the top corner from 12 yards before being dismissed and Argyle's David Norris had a late effort ruled out for offside.
Southampton boss George Burley
"There were a lot of tired legs out there. That's our second game in three days on rain-sodden pitches. "We are pleased to get a point because we never got our game going at all.
"But under the circumstances I think it is hard to be critical when you have put so much in with the two games in three days. It's not easy."
Plymouth: Larrieu, Gosling, Doumbe (Summerfield 35), Seip, Sawyer, Norris, Buzsaky (Dickson 80), Nalis, Capaldi, Samba (Reid 55), Hayles.
Subs Not Used: McCormick, Aljofree.
Sent Off: Hayles (84).
Booked: Norris, Hayles, Buzsaky.
Goals: Hayles 66.
Southampton: Davis, Ostlund, Lundekvam, Baird, Bale, Prutton (Makin 46), Wright, Pele, Skacel (Licka 46), Wright-Phillips (McGoldrick 80), Rasiak.
Subs Not Used: Bialkowski, Sarmiento.
Booked: Bale, Davis, Pele.
Goals: Rasiak 5.
Att: 15,377
Ref: K Wright (Cambridgeshire).