The 26-year-old came to the crease with his side in trouble at 3-36 early on Friday at Karen Rolton Oval before reeling off an impressive 115, that included 16 fours and two sixes.
The Redbacks were all out for 373 just before stumps and hold a 104-run lead, with NSW 1-0 in their second innings.
Blues opener Ryan Hadley lasted just six deliveries and was caught down the leg-side on the final ball of the day.
South Australia resumed in the morning at 1-20 after losing Test opener Travis Head in the shadows of stumps on Thursday.
Sangha combined with Henry Hunt (43) in a 108-run stand and then teamed up with Test wicketkeeper Alex Carey (58) for another century-plus stand.
He was out in inglorious fashion after hitting a leg-side full toss by part-time spinner Kurtis Patterson straight to Charlie Stobo in the deep.
It was Patterson's maiden first-class wicket in his 119th game and only the second time he's bowled at domestic level.
Allrounder Liam Scott chipped in with an aggressive 61 from 78 deliveries to inflict some pain on NSW late.
Quick Liam Hatcher was the best of the visitor's bowlers with 4-116, while 22-year-old left-arm finger spinner Joel Davies took 3-55.
Third-placed South Australia and fourth-placed NSW are in the hunt for a spot in the Shield final in the penultimate round, with runaway competition leaders Victoria already securing their spot.
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