The Blues were skittled by a Gary Putland-inspired attack for a miserable 148 in their second innings, setting a meagre target of 96.
Ben Rohrer produced one of the few fighting efforts for NSW before getting a questionable lbw decision to be out for 40.
But he reckons the demons in the wicket which contributed to the NSW collapse should give their bowlers hope of producing something spectacular on Wednesday.
"The way we've played our cricket this year, we're always trying to win games and we always think we can.
"If we can do ... take four or five wickets in that first hour, you never know.
"There's enough playing tricks in the batsman's mind that we can start to put the dressing room under pressure if we can get a few of these good players out early."
South Australia had cruised to first-innings points on day three at the SCG when their tail wagged - their final five wickets adding 151 to help them post 426 for a 53-run lead.
But efforts before and after tea look certain to deliver them an outright victory, destroying the NSW top and middle order to leave them reeling at 6-75.
It puts the second-placed Redbacks in the box seat for maximum points and outright first on the Shield ladder, after entering this clash trailing the Blues by just two points.
"We've still got to bat well. The wicket is spinning and keeping low now," Putland said.
Led by Putland (4-35), South Australia made short work of the Blues' top order to have the home side struggling at 3-27 by tea.
Chadd Sayers (2-13) sent the stumps of Nic Maddinson (0) flying in the first over of the innings before Putland took over.
He had Scott Henry caught at third slip by Johan Botha for one and, soon after, trapped in-form opener Ryan Carters (4) lbw to have the Blues reeling at 3-11.
But worse was to come, with Redbacks skipper Botha grabbing the crucial wickets of Moises Henriques and Rohrer, who had combined for a first-innings partnership of 187.
Rohrer initially stood his ground to express displeasure at the decision, and replays suggested he had reason to be aggrieved - with the ball hitting high on his pad.
"It missed the pad entirely, but that's cricket," he said.
A rearguard action from all-rounder Sean Abbott (27), Steve O'Keefe (15) and debutant Manjot Singh (19) ensured play would advance to a fourth day.
Earlier, Kane Richardson hit a sparkling run-a-ball 40 to put on a 74-run eighth-wicket partnership with Joe Mennie (45) to secure first-innings points.