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Mauricio Pellegrino's side trailed to Ryan Fraser's goal late in the first half, but Austin nabbed an important point with his third goal in as many games.
The result means Bournemouth climb to 14th in the table, five points above the relegation zone, while Southampton move up to 11th.
Striker Austin saved a point for the Saints thanks to an assist from Nathan Redmond just days after the winger was on the receiving end of a bizarre exchange with Manchester City boss Pep Guardiola.
Guardiola was seen shouting at Redmond after the final whistle of City's 2-1 win over Southampton on Wednesday, but the Spaniard and the Saints winger both said the heated exchange was actually complimentary.
Redmond might still have been keen to prove a point, particularly after Pellegrino left him out of the starting line-up at Dean Court.
Austin's goal came in only his second Premier League start this season, giving Saints encouragement that he can be the solution to their scoring problems.
Virgil van Dijk had an early sight of goal but headed wide before Saints goalkeeper Fraser Forster made an excellent reaction save at the other end to deny Jermain Defoe.
It was a defensive error that prompted the 42nd minute opener.
Wesley Hoedt had twice turned his way out of trouble but a third risk proved one too many as Josh King nicked possession before Andrew Surman rolled left to Fraser, who stroked the ball past Forster.
Redmond replaced James Ward-Prowse at half-time on the right of the attacking three and Southampton equalised in the 61st minute.
Bournemouth's Lewis Cook dallied on the edge of the area and Oriol Romeu nipped in to pick out Redmond, whose low cross was steered home by Austin.
