The Saints extended their lead after Filo Tiatia was penalised for holding on, and Myler made no mistake with his second penalty.
Wales lock Ian Gough was forced to leave the field in the 35th minute with a shoulder injury, but put that setback behind them when hooker Richard Hibbard drove over. With Gareth Owen adding the conversion, the Ospreys found themselves 7-13 at the break.
Myler's unerring boot continued to keep the scoreboard ticking over with another well struck penalty after Cai Griffiths had been penalised for bringing down the scrum.
Replacement winger Jonathan Spratt made an instant impact by scoring a try for the Ospreys with his first touch. Owen's conversion inched the Ospreys towards the Saints.
The Ospreys remarkable comeback saw them take the lead with another Owen penalty but with 10 minutes remaining Myler once again struck with his deadly boot to guide the Saints to safety.