The NSW side raced on to 233 for two at stumps on Thursday.
Bracken ripped through the South Australians who were all out in just 80 minutes and 14.4 overs.
NSW opener Phil Jaques was unbeaten on 154 at stumps.
Five of SA batsmen made ducks -- Tom Plant, Mark Cosgrove, Callum Ferguson, Mark Cleary and Shaun Tait. SA set a record for the most ducks, six, in an innings in the corresponding game last year.
SA were 24 for nine but scrambled past the lowest-ever Sheffield Shield score of 27, set by SA against NSW at the Sydney Cricket Ground in 1955-56.
In other Shield action, Queensland wrapped up a commanding seven wicket victory over Tasmania in the match at the Gabba in Brisbane.
Queensland needed just 16.5 overs to haul in Tasmania's lead of 85 despite losing batsmen Maher, Clinton Perren and Andrew Symonds early in the chase.
It was the third outright win of the season for Queensland, who continue to dominate at state level after winning five Sheffield Shield titles over the past decade.
Victorian fast bowler Shane Harwood suffered a suspected fractured cheekbone on day two of the match against Western Australia at Melbourne's Junction Oval.
Harwood retired hurt when he was struck in the face by a Kade Harvey bouncer in Victoria's total of 152 for nine. He was taken to hospital.
WA were 63 for no wickets in their second innings at stumps, with Chris Rogers 44 not out and Michael Hussey 19 not out, and in a commanding position with a 188-run lead at the halfway point of the match.
Earlier, WA batsman Murray Goodwin hit a fine 130 and gained the support of a wagging tail to steer his side to 277, with Beau Casson (31), Brett Dorey (17) and Steve Magoffin (16) all contributing.
In Brisbane (day four): Queensland 384 (J. Maher 148, A. Bichel 69; A. Griffith 5-109) and 87 for 3 (C. Philipson 39 not out, S. Watson 32 not out; A. Griffith 2-24) beat Tasmania 216 (D. Wright 71 not out; J. Hopes 3-23) and 253 (M. Bevan 93, T. Birt 48; A. Bichel 5-70 by 7 wkts.
In Melbourne (day two): Western Australia 277 (M. Goodwin 130, S. Marsh 34; S. Harwood 3-50, M. Inness 3-68) and 63 without loss (C. Rogers 44 not out, M. Hussey 19 not out) v Victoria 152 for 9 (M. Elliott 65, C. White 39; B. Dorey 3-26, B. Edmondson 3-42)
In Sydney (day one): South Australia 29 (N. Adcock 8; N. Bracken 7-4) v New South Wales 233 for 2 (P. Jaques 154 not out, D. Thornely 37 not out)