With no result in sight due to Monday's rain, play ended at 1.50pm on day five after both teams sought permission from Cricket Australia to call it off early.
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Only 24 wickets fell in the match that was played at a slow pace on the placid Manuka Oval surface with a slow outfield.
The Blues only needed a draw to claim the Shield for the first time since 2008.
NSW captain Steve Smith reached his 13th first-class century when his unbeaten 103 helped NSW to 4-197 in the second innings – an overall lead of 464.
The players walked off 10 minutes after Smith reached three figures with man-of-the-match Moises Henriques 10 not out.
A classy first innings ton from Test squad all-rounder Henriques put the match out of WA's reach, while a six-wicket haul to paceman Josh Hazlewood made the result a formality.
The match was played in Canberra due to a scheduling clash with the one-off Major League Baseball match at the SCG.
On day two, NSW all-rounder Stephen O'Keefe received a fine for breaching the Cricket Australia code of behaviour.
O'Keefe accepted a 20 per cent fine of his match fee for abuse of equipment in the player's race after he was dismissed in a tight lbw decision.