NSW, with Konstas unbeaten on 109, are 2-191 in their second innings at stumps on day two, a lead of 70 runs in Sydney.
The Blues were bowled out for 204 in their first dig and SA, powered by Jake Weatherald's 142, replied with 325 all out.
But Konstas was key in erasing NSW's deficit, combining with Kurtis Patterson for a vital 117-run partnership for the second wicket.
Patterson made 43 before falling caught-and-bowled by spinner Ben Manenti, diving forward to complete an excellent low-down catch.
Konstas survived a confident caught behind appeal when on 14 from Wes Agar's bowling.
On 21, he hooked Agar and was caught at deep square leg - but the umpire called a no ball.
And on 69, Konstas had another stroke of fortune when dropped by Jason Sangha at first slip from Manenti's bowling.
The 21-year-old registered his sixth first-class century from 129 balls to ensure he's firmly in the reckoning for Australia's Test squad to meet New Zealand.
Dumped by national selectors in July last year after five Tests, Konstas has now scored 71, 151 not out, 5, 2, 24 and Thursday's ton in the Shield this season, plus 149 for the Blues in a 50-over match.
Earlier, SA's lead was underpinned by the stellar knock of Weatherald, who was aghast to be adjudged caught behind from a Jake Scott short ball.
The lefthander dropped his gloves to the delivery which appeared to brush his forearm: when given out, he put his hands on his helmet and bent over in disbelief before storming off the field.
Weatherald's departure left the visitors 7-236, but there was no quick kill for the Blues bowlers, as SA allrounders Manenti and Noah McFayden increased the lead.
Manenti (40) and McFayden (43) put on 57 runs for the eighth wicket to frustrate the Blues.
Veteran NSW quick Sean Abbott returned the best bowling figures with 3-41 from 15 overs, while Ben Dwarshius (3-72), Scott (2-46) and Liam Hatcher (2-46) also took multiple wickets.
Test spinner Nathan Lyon (0-82 from 25 overs) failed to find form after his middling tour of South Africa.
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