After losing the toss NSW went to lunch on day one at 2-65.
Kurtis Patterson (17no) and Jason Sangha (12no) were at the crease after Blake Nikitaras (20 off 58 balls) and Daniel Hughes (15 off 58) departed in the morning session.
NSW crawled to 0-30 off 18 overs before Morris inflicted his double blow.
Hughes was the first to fall when he struck Morris straight to mid-off, and the Blues were 2-37 when a diving Joel Paris took a sharp catch at gully to dismiss Nikitaras.
Morris went to lunch with the excellent figures of 2-10 off five overs while Matthew Kelly (0-8 off six) was also miserly.
The Warriors kicked off their title defence without star duo Shaun Marsh (knee) and Jhye Richardson (rested).
Marsh, who dislocated his knee in WA's one-day final triumph last summer, is still recovering but expected to return soon.
Richardson, on the comeback trail from a hamstring injury, snared 4-24 in WA's nine-wicket one-day triumph over NSW on Saturday.
Although the 26-year-old has been rested for the season-opening Shield clash, he is keen to make red-ball cricket his focus this summer in a bid to break back into the Test team.
NSW will be aiming to make up for the weekend's one-day flop against WA.
The Blues were 6-20 at one stage before being rolled for 76, with WA needing just 17 overs to reach the victory target.
NSW paceman Ben Dwarshuis, who featured for Australia's T20 side in Pakistan recently, was named for his Shield debut at the age of 28.
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