The Blues led by 272 runs when they declared at 8-373 in their second innings on Tuesday's fourth day, but narrowly ran out of time to skittle their visitors despite a late flurry of wickets.
Western Australia finished at 9-139 in their second dig, withstanding a nervy collapse of 3-4 in the final hour and then a ninth wicket that fell with the fourth-last ball of the day.
The visitors were 134 shy of their target when Joel Davies (2-30) bowled the final delivery of the Shield's regular season.
A draw appeared likely from the start of WA's second dig given the Blues needed 10 wickets in two sessions after declaring at lunch.
But NSW dared to dream as big guns Cameron Green (25) and Sam Whiteman (24) fell in consecutive overs just after tea to leave WA at 4-78.
Green, who endured a tough Test summer, skied Davies to long-on with the first delivery he faced in the match's final session so could not reprise his century from the first innings.
WA managed to steady the ship before Liam Hatcher (3-24) had the breakthrough sixth wicket around 5.45pm when Joel Curtis (18) edged to the slips.
Hatcher's 43rd scalp made him the Shield's leading wicket-taker for the summer, and when Jhye Richardson edged to gully two overs later, the Blues had a sniff.
WA were eight down as stand-in skipper Sean Abbott (1-23) bowled quick Joel Paris and ran down the wicket in celebration.
With shadows falling on the ground at Cricket Central, NSW were forced to bring on the spinners to complete the required overs.
Davies bowled No.10 Cameron Gannon on the fourth-last ball of the day, but the final wicket proved elusive as the entire Blues outfit crowded around tailender Corey Rocchiccioli at the crease.
The draw and Tasmania's earlier defeat of Queensland meant NSW finished the season second-last on the ladder.
Tuesday's result also confirms consecutive wooden spoons for Western Australia, who had been firmly entrenched on the bottom of the ladder.
The match was the last in Greg Shipperd's 11-year stint with Cricket NSW, which began when he joined the Sydney Sixers as head coach in 2015.
He started coaching the Blues in an interim capacity in November 2022 before taking the post full-time in May 2023 but couldn't lead the powerhouse side to a Shield final in that time.
Back-to-back wooden spooners WA will also turn over a new leaf next summer as Adam Voges steps down as coach. He will be replaced by one-Test wonder and former assistant Beau Casson.
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