Don Cowie's visitors remain 10th, below Kilmarnock on goal difference, a point above Dundee and six clear of bottom side St Johnstone.
St Mirren were guilty of not clearing their lines at the County opener after Zac Ashworth's cross. Connor Randall nodded across for White, whose effort and that of Josh Nisbet were blocked before Hale lashed the ball past Zach Hemming.
Hale threatened again with a shot and Nohan Kenneh also tested Hemming before the hosts levelled.
Boyd-Munce picked up from Ayunga's lay-off outside the box and drilled an effort beyond Amissah.
Now it was St Mirren creating the chances and Mark O'Hara lifted one over before another Boyd-Munce effort was blocked by Amissah.
The balance of play had shifted and the Buddies kept up their momentum after the break with Boyd-Munce's superb pass finding Ayunga and the striker scoring at the second attempt after Amissah had come off this line.
Ashworth also played a role in the second County goal, his deep corner from the right headed back across goal by White and crossing the line despite Boyd-Munce's attempted clearance.
But St Mirren were not to be denied and the home support erupted in celebration after Idowu's precious winner.