Dunith Wellalage, Wanindu Hasaranga and Maheesh Theekshana shared six wickets as they bowled out New Zealand for 135 in 19.3 overs on Saturday.
New Zealand fast bowler Zakary Foulkes picked up three wickets in three overs but Sri Lanka captain Charith Asalanka's unbeaten 35 — the game's top score — carried Sri Lanka to 6-140 with an over to spare.
"Bit of nerves, but my plan was to bat till the end," Asalanka said.
"We could have bowled them out 15-20 runs before, (but) credit should go to their lower order batters."
The second and final game will be played at the same venue on Sunday. Both teams then play three ODIs to prepare for next year's Champions Trophy.
New Zealand stumbled to 31-3 inside the batting powerplay.
"I thought we did pretty well to get to 130, it looked like we wouldn't get there halfway through," captain Mitchell Santner said.
"It was a spinning wicket to be fair. We felt that we could defend it, but a couple of good knocks take it away from you."
Tim Robinson was clean bowled off Wellalage's (20-3) quick arm ball and Mark Chapman flicked fast bowler Nuwan Tushara to Hasaranga at deep square leg.
Opening batter Will Young smashed a six and a four in his run-a-ball knock of 19 but missed Theekshana's (21-1) fuller ball and was adjudged leg before wicket.
Hasaranga (20-2) and fast bowler Matheesha Pathirana (29-2) further squeezed New Zealand in the middle overs.
Glenn Phillips was baffled by Hasaranga's googly and was trapped lbw on the back foot, and wicketkeeper Pathirana caught Mitchell Hay off a thick outside edge.
Santner missed Hasaranga and was stumped as New Zealand fell to 6-96-in the 16th over. Foulkes' quickfire unbeaten 27 off 16 lifted the total before Wellalage wrapped up the innings by claiming the last two wickets off successive deliveries.
Sri Lanka stumbled early in the run chase when Santner had Kusal Mendis lbw in his first over.
Pathum Nissanka (19) went for an extravagant inside out shot off Foulkes' last ball in the powerplay and was clean bowled, while Kusal Perera (23) couldn't read an arm ball from Michael Bracewell and was lbw.
Perera became Sri Lanka's top run-scorer in T20s, surpassing Tillakaratne Dilshan's 1,889.
Asalanka, the player of the match for his 28-ball knock, held up one end by hitting two sixes and a boundary despite Foulkes getting Bhanuka Rajapaksa caught behind off a short delivery.
And Hasaranga (22) mistimed a pull shot against the right-arm fast bowler when Sri Lanka needed 11 for victory.
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