Resuming their second innings at 2-50 and chasing 289, SA were bowled out for 191 on Saturday at Cricket Central.
Test great Nathan Lyon snared three wickets, while Jake Scott took four and fellow paceman Liam Hatcher also chimed in with three.
After starting the season with an innings win over Victoria, SA have lost their past three matches and the two-time defending Shield champions have slumped to second-bottom.
It is also the first win for NSW at the Cricket Central venue. They improved to fourth after last week's innings loss to Tasmania in Hobart.
"It was a pretty tough week in Tassie ... we were after a bit of a response this week and we played from behind for most of the game - so I'm really proud of the effort," NSW captain Nic Maddinson told ABC radio.
Most of the SA top order made starts in their second innings, but no-one was able to build the big knock they needed.
Sam Konstas was named man of the match for his crucial second-innings 173. Along with taking the game away from SA, Konstas's highest first-class score gave his Test squad recall hopes a massive boost.
"He's an extremely hard worker at his game. Obviously he's still extremely young and inexperienced ... but I feel like he's trying to find a method that works for him," Maddinson said.
"He's a guy who just makes 100s. That's pretty special - there aren't many of them going around."
SA captain Nathan McSweeney noted they lost their first two Shield games last season before going on to beat Victoria in the final.
"I said to the boys just then, we won four games last (season) and won the Shield final - it's a really hard competition," he said.
"There are small margins involved, so we have to make sure and look back on what we do really well and try to execute that next week," he said.
Jake Weatherald added seven to his overnight score before Lyon trapped him lbw for 38. It proved a massive breakthrough and he was SA's top scorer as wickets fell steadily.
Weatherald also top-scored in their first innings with 142 - his first century since being dropped from the Test team.
"You can be in the washing machine a little bit after playing for Australia after being spat out," McSweeney said of Weatherald.
"The way he's worked on his game, mentally and technically, to come out with such intent and confidence in his game, it's really nice to see him get reward."
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