The left-arm seamer claimed the last five wickets to finish with 5-36 off 14.2 overs to dismiss the South Australians for 172 off 50.2 overs on Friday.
Champions NSW claimed six outright points to go top of the standings with Victoria after the opening round of matches.
Bracken was Thursday named in a 12-man Australian squad for next week's opening Test match against the West Indies in Brisbane where he is likely to play in seaming conditions at the Gabba.
South Australia, chasing 360 runs to win, fell away early on the final day losing their last six wickets for 58.
Former Test batsman Darren Lehmann again topscored for his state with 47 off 55 balls following on from his 159 in the first innings.
Test batsman and NSW skipper Simon Katich was named man-of-the-match with his batting double of 144 and 79 not out, while leg-spinner Stuart MacGill finished with five match wickets for 191 off 37 overs.
NSW travel to play Western Australia in Perth from November 6-9, while South Australia have a home match with Queensland at the same time.
New South Wales 515 for 9 declared (S. Katich 144, M. Clarke 178, P. Jaques 69; D. Cullen 4-149, P. Rofe 3-109) and 187 for 2 declared (S. Katich 79 not out, P. Jaques 66) beat South Australia 343 (D. Lehmann 159, M. Cleary 52; B. Lee 4-77, S. MacGill 3-131) and 172 (D. Lehmann 47, C. Ferguson 44; N. Bracken 5-36, G. McGrath 2-35, S. MacGill 2-60) by 187 runs.