The Cherries enjoyed the better of the chances in the first half and were perhaps unlucky not to be awarded a penalty when Adam Smith went down under a Sofiane Boufal challenge.
The hosts took the lead on 42 minutes as Fraser converted an Andrew Surman cross after a mistake at the back by Wesley Hoedt but Southampton improved after the break.
Manager Mauricio Pellegrino replaced James Ward-Prowse with Nathan Redmond at the interval and his introduction proved key as he provided the assist for Austin, who hit a sweet first time shot beyond Asmir Begovic in the Bournemouth goal with an hour gone.
Saints appeared the more likely to go on and win the game after they restored parity and Ryan Bertrand saw an effort go just wide of the target a few minutes after the equaliser.
Austin had two decent chances in the final 10 minutes but he headed over the bar and was then denied by Begovic as the two sides had to settle for a point.