Redbacks stand-in captain Jake Lehmann steadied the ship for SA after the hosts flirted with danger during a final-day collapse of 5/27.
SA was set a target of 253 shortly before tea on Friday, when Blues skipper Peter Nevill declared at 8/279 after producing a captain's knock of 72 not out.
The Redbacks lost Jake Weatherald and Callum Ferguson in a six-over burst before tea.
The home side crashed to 5/41 in 15.3 overs then 6/74 but Lehmann refused to fold, reaching stumps unbeaten on 33 to ensure his team salvaged a draw.
Lehmann soaked up 126 deliveries, standing up in his first Shield game as skipper, while Joe Mennie successfully survived 51 balls.
The sides shook hands when the Redbacks reached 6/103 from 44.3 overs.
Former Test paceman Trent Copeland snared match figures of 9/131.
Copeland collected 6/86 in SA's first dig, including his 300th first-class wicket, then removed openers Weatherald and Conor McInerney to give NSW a genuine sniff of victory on day four.
Copeland later returned to the attack and set the stage for a dramatic finish, trapping Cameron Valente lbw for 24 late in the session.
Copeland also helped himself to 64 runs in the game, finishing not out in both digs.
NSW struggled early on Friday morning, having resumed at 3/84 in the second innings then slipped to 5/121 when Nevill strode to the crease with the game in the balance.
The former Test ‘keeper slowly but surely swung momentum, sharing key partnerships with debutants Jack Edwards, Jason Sangha and Daniel Sams.
Chadd Sayers, who finished with figures of 5/101, dismissed nightwatchman Abbott, opener Nick Larkin and Edwards in the morning session and claimed his 250th first-class wicket during the contest.
South Australia host Queensland at Adelaide Oval next Thursday in the Redbacks’ next Sheffield Shield clash.