In a poor first half, Saints keeper Kelvin Davis saved twice from Ade Akinbiyi, before top scorer Grzegorz Rasiak headed Gareth Bale's cross wide.
Burnley threatened after the break when Davis tipped over Wade Elliott's shot and then saved well from Kyle Lafferty.
Saints could have won it but Bradley Wright-Phillips' header was saved by Mike Pollitt and he then fired wide.
Burnley boss Steve Cotterill:
"It was an excellent point for us to get today and I am a very happy manager at the moment.
"I was delighted with the way my two new players Ade Akinbiyi and Michael Pollitt slotted straight into he side.
"It was pleasing to keep a clean sheet and that will build confidence for the rest of the season. The players have really performed well for me today."
Southampton: Davis, Baird, Powell, Lundekvam, Bale, Licka, Wright, Pele, Jones (Wright-Phillips 46), Rasiak, McGoldrick.
Subs Not Used: Bialkowski, Ostlund, Lallana, Viafara.
Burnley: Pollitt, Thomas, Duff, McGreal, Harley, Elliott, James O'Connor, McCann, Djemba-Djemba, Akinbiyi, Lafferty.
Subs Not Used: Jones, Garreth O'Connor, Spicer, Noel-Williams, Foster.
Booked: Harley, Elliott.
Ref: A Bates (Staffordshire).