Blues vice-captain Jason Sangha was ruled out before play resumed on Wednesday after being concussed during the warm-up, and things continued to go downhill from there.
NSW moved to a steady 0-48 in their second innings before a collapse of 4-16 sparked a dramatic downfall, with the Blues eventually bowled out for 162.
It set WA a victory target of just 85, and the home side chased down the total an hour before scheduled stumps on day three.
WA had plenty of contributors across the three days, but two players in particular stood out.
WA teenager Wyllie was the hero of day two, scoring 104 off 204 balls to dig the Warriors out of trouble.
At 18 years and 163 days, Wyllie became the youngest player to reach triple figures in Shield cricket since Ricky Ponting, who was 18 years and 40 days when he notched his maiden ton in the competition.
His knock helped lift the Warriors to 258, giving them an invaluable 78-run first-innings lead.
Another emerging star - Warriors paceman Morris - was also influential in the victory.
The 24-year-old followed up his haul of 5-36 in the first innings with 4-46 in the second dig, giving him match figures of 9-82.
The performances of Wyllie and Morris not only guaranteed victory for the Warriors, but also showcased the enviable depth of WA cricket.
Allrounder Aaron Hardie chipped in with 2-31 in NSW's second innings, while Joel Paris bowled nine maidens on his way to the incredible return of 1-4 off 13 overs.
"I think the difference in the game were the partnerships late on day two," stand-in WA skipper Sam Whiteman said.
"Joel Paris got 25 and Matt Kelly got 47, which helped Teague get his maiden first-class hundred, which was pretty special to watch.
"I'm sure it's the first of many. Getting that 78-run lead was huge."
NSW were bowled out for 180 on day one and they were a shambolic 5-66 in the second innings before Baxter Holt (54 off 78 balls) helped them add respectability to the scorecard.
Overall it was a disastrous week for NSW in Perth, which started with an embarrassing nine-wicket one-day loss to the Warriors.
The Blues were 6-20 in that match before being rolled for 76, with WA reaching the target in 17 overs.
"Really disappointing. I just thought our batting display today on what turned out to be a pretty good wicket was just flat-out not good enough to be honest," NSW captain Kurtis Patterson said.
