Bournemouth's Ryan Fraser curled home the opener in the 42nd minute of an even first half after Southampton defender Wesley Hoedt, guilty of overplaying, was dispossessed by Joshua King.
Southampton began to dictate proceedings after the break and the in-form Austin -- who scored a brace against Everton last weekend -- restored parity with a smart finish from substitute Nathan Redmond's low cross in the 61st minute.
Austin, who has scored seven goals in his last 10 league starts, twice had chances to win it for Southampton while Bournemouth substitute Callum Wilson was unable to control a loose ball with the goal at his mercy.
After Austin's double against Everton, Southampton manager Mauricio Pellegrino said the striker's form would be crucial during December.
On Sunday, he was the most threatening player on the pitch, combining his physical presence with smart movement and incisive finishing.
"Going in at half-time 1-0 down we were not good enough in the first half but we stepped up in the second and looked like we were going to nick it," Austin told Sky Sports.
"Instead it's a point away from home going into a big December. I should have scored a near-post header but these things happen. I was still in the right place at the right time.
"I've just got to score goals, work hard and help us win games. We've got a lot of big games coming up."
Bournemouth were aggrieved not to receive a penalty when Adam Smith was booked for diving despite apparent contact from Sofiane Boufal.
Instead referee Jon Moss issued a yellow card but he later admitted getting the decision wrong.
"I spoke to him after and he apologised and said it was a penalty," Smith told Sky Sports.
"For the ref to book me doesn't help because that's my fifth yellow card of the season. I don't mind him admitting it but the fact that he booked me and can't get it rescinded, I'll miss the next game.
"If we had got the penalty maybe we would have gone and scored another one. But we got a point and need to look forward now."
Southampton climb one place to 11th with 17 points -- two points and three places above Bournemouth.
(Reporting by Tom Hayward; Editing by Toby Davis and Clare Fallon)
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