Chasing 275 for victory, Sri Lanka were bundled out for 76 in the 20th over with Shipley orchestrating their rout on a lively track at Eden Park.
Only three Sri Lankan batters managed double digits in their sorry-looking scorecard.
Earlier put into bat, New Zealand were all out for 274 with three deliveries left in their innings.
Five home batters got past 25 but opener Finn Allen's 51 was the highest score by a New Zealander.
Daryl Mitchell made 47 and Glenn Phillips contributed 39, while Rachin Ravindra (49) fell agonisingly short of a half-century in his maiden one-day international.
Chamika Karunaratne was pick of the Sri Lankan bowlers claiming a career-best 4-43 on a lively pitch at the Eden Park.
Playing his first ODI in two years, former captain Angelo Mathews found himself tasked with reviving Sri Lanka who lost both their openers inside four overs.
The wobble became a full-blown crisis with Shipley reducing Sri Lanka to 31-5 inside 10 overs.
The 26-year-old removed Charith Asalanka and Sri Lanka skipper Dasun Sanaka with successive deliveries but Karunaratne denied him a hat-trick.
Blair Tickner trapped Mathews lbw for 18, which turned out to be the highest score by a Sri Lankan.
The second ODI of the three-match series is scheduled in Christchurch on Tuesday.
