The Sri Lankans, who lost the toss and were put into bat, were bowled out for a modest score of 119 before New Zealand managed just 60 runs from 15 overs in response.
Mahela Jayawardene top scored for Sri Lanka with a knock of 25, while Lahiru Thirimanne (20), Sachithra Senanayake (17), Kusal Perera (16) and Thisara Perera (16) also helped push their team past the 100-run mark.
Luke Ronchi (two), Nathan McCullum (two) and Kyle Mills (four) did little to stop the New Zealand collapse, and their defeat was confirmed when Boult was dismissed for three runs. Final batsman Corey Anderson was absent due to injury.
Herath finished the match with impressive figures of 5-3, while Senanayake claimed the other two wickets.