Needing an outright win to boost their chances of making the final, the Blues ran out of time to secure victory as they battled to dismiss SA in their second innings on Monday.
Both captains shook hands midway through the 93rd over, with the Redbacks finishing on 9-259, leading by just 36.
NSW had hammered home their advantage in the morning after beginning the fourth and final day at Cricket Central on 8-465.
Allrounder Chris Green (63 no) pushed the Blues to 8-510, a first-innings lead of 223, before captain Moises Henriques declared.
SA ran into early trouble in their bid to save the match, collapsing to 2-2.
Highly-touted youngster Jake Fraser-McGurk, who has been tipped by greats such as Ricky Ponting to be a three-format player for Australia, fell for just two.
It continued a lean run at Shield level for Fraser-McGurk, making scores of 0, 1, 16 and 2 across his last four first-class innings since making his debut for Australia in last month's ODIs against West Indies.
But No.3 McSweeney proved to be a rock for the Redbacks, facing 242 balls for his 67 to frustrate the NSW attack.
It came after McSweeney saw off 178 balls for his 53 in SA's first innings.
The combined 420 deliveries was the most balls any player has faced in a Shield match this season, passing Queensland veteran Joe Burns (401 against Tasmania in October).
Thomas Kelly (69) and captain Jake Lehmann (56) also put in handy knocks to help SA avoid defeat.
But the Redbacks did suffer some nervous moments when McSweeney was dismissed after they hit the lead in the final hour of the match.
Towering NSW allrounder Jack Edwards (4-59) was on a hat-trick after cleaning up quicks Wes Agar and Spencer Johnson with 20 minutes remaining.
NSW will have to beat Queensland at Allan Border Field in their last regular season match, starting next Monday, to be any chance of qualifying for the final.
Whatever the outcome of that match, NSW will have to be satisfied given the dire position they started the season.
The Blues went 21 months without a Shield victory, with their 15-match winless streak the worst in their proud history.
But an upset win over dual reigning champions Western Australia in November sparked a major revival for the traditional cricket powerhouse.
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