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.
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.