Southampton kicked off their Europa League campaign with a comfortable 3-0 victory over Sparta Prague at St Mary's on Thursday night.
The opening goal came in just the 5th minute when a penalty was awarded as Austin's attempted cross was blocked by the arm of a sliding Costa Nhamoinesu.
There was some confusion over who would take the penalty as Dusan Tadic tried to wrestle ball away from Austin but Virgil van Dijk intervened, prompting the Englishman to step up and fire beyond Tomas Koubek.
Just over 20 minutes later and the Saints were two to the good when Cuco Martina, whose initial cross was blocked, found Austin with a clever ball allowing the striker to head home his second despite the best efforts of Koubek.
Southampton had to wait until injury time to well and truly wrap up proceedings when Rodriguez produced an expert finish from a Shane Long pass to score his second goal in as many outings at St Mary's.
The victory will give Puel's men confidence heading into Sunday's home Premier League clash with Swansea City prior to their next Group K fixture against Israeli outfit Hapoel Be'er Sheva, who upset Inter Milan 2-0, which takes place on September 29.
2016/17 UEFA Europa League - Group K
St Mary's Stadium, Southampton, England - 25,125