At stumps, NSW were 150 for 2 in their second innings after bowling South Australia out for a miserable 135 in their first innings of the four-day game.
NSW then opted not to enforce the follow-on, despite holding a 163-run first innings lead.
Paceman Matthew Nicholson ripped apart the South Australian top order, taking 4-36 while spinner Stuart MacGill cleaned up the tail with 3-17.
For South Australia, Greg Blewett with 42 and Nathan Adcock on 21 were the only players to reach 20.
In Hobart, a 98-run seventh-wicket stand between Sean Clingeleffer and Damien Wright saved face for Tasmania on day two of the match against Queensland at Bellerive Oval.
With Tasmania struggling on 179 for 6 after some dour batting, the keeper and quick bowler added almost 100 runs to lift the team to 294 for 8 at stumps chasing Queensland's first innings of 401.