The tourists were edged by eight runs chasing 8-172 in the first match two days earlier and again faltered late while pursuing New Zealand's 5-186 on Monday. Sri Lanka were all out for 141 in 19.1 overs.
"It's really important to finish the game, no matter how it started," Sri Lanka captain Charith Asalanka said.
"The way you finish is the most important thing. In the first game we were almost there to win and again we're disappointed."
Once again, Jacob Duffy was New Zealand's key bowler, dismissing opener Pathum Nissanka for 37 and returning to remove Kusal Perera for 48, after both batters looked well placed to steer Sri Lanka to victory.
Nissanka made 96 in the first match in a 120-run opening partnership with Kusal Mendis before Duffy turned that match in New Zealand's favour when he took three wickets in four balls to stifle the Sri Lanka chase.
He took 4-15 Monday to once again stand out as the difference between the teams.
After dismissing Nissanka, Duffy produced a superb yorker to remove Perera in the 16th over when Sri Lanka were 4-127 and still in with a chance.
He then removed Wanindu Hasaranga (1) and Maheesh Theekshana (0) in the space of three balls in the 18th over as the Sri Lanka tail again failed to fire.
Matt Henry took two wickets with consecutive balls in the 19th over before Zak Foulkes finished off the Sri Lanka innings with five balls remaining.
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