WA declared at 4-346 in their second innings soon after lunch on day four, leaving NSW a victory target of 282 from 57 overs.
The Blues weren't interested in the run chase, with the visitors content to do their best to grind out a draw.
Konstas crafted 50 off 107 balls to help NSW recover from 1-0 to reach 4-130 by the time the two captains shook hands on Sunday evening with two overs remaining.
Ladder leaders South Australia (51.76 points) have already earned hosting rights for the Shield final given they are guaranteed to finish on top, irrespective of what happens in the final round.
The race for second spot will be between second-placed Queensland (36.8 points), third-placed NSW (35.39), fourth-placed WA (34.43) and fifth-placed Victoria (32.49).
South Australia take on Queensland in Adelaide next week, while WA host Victoria and NSW visit Tasmania.
Hilton Cartwright was the standout in WA's second innings, with a career-high 171 not out off 294 balls featuring 19 fours and a six.
Cameron Bancroft, in his return from the fractured shoulder suffered during a sickening collision in the BBL, scored a patient 86 off 277.
NSW's chase started disastrously, with Nic Maddinson edging Joel Paris to slip on the third ball of the innings.
It was 2-50 in the 25th over when Kurtis Patterson was bowled by Joel Paris (2-8) for 13.
Konstas held the innings together with a crucial half-century.
But the 19-year-old's decision to trot down the pitch to block spinner Corey Rocchiccioli proved to be his undoing, with Konstas stumped well out of his crease.
When Rocchiccioli had Josh Philippe caught next ball, NSW were 4-86 and a tad vulnerable.
Matthew Gilkes (53no) and Oliver Davies (11no) held off WA's charge, ensuring NSW escaped with a draw.
"Five an over was probably a bit too much," NSW allrounder Jack Edwards said.
"They probably batted us out of the game. Losing the early one as well, we decided to pack it up.
"He (Konstas) played well. It was good to see him apply himself and show us how much of a good, natural player he is when he's applying himself.
"It was a nice knock, and hopefully next time he can make it a really big one."
Cartwright said WA were wary not to hand NSW an easy run chase.
"We wanted anywhere between 250-300," he said.
"Last night just before they had the new ball, it was really easy to score when that ball got soft, so we didn't want to give them too many overs with not enough runs.
"If we gave them 70 overs to chase 250, it probably would have been quite easy for them."
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