Sri Lanka captain Angelo Mathews was 39 not out with Lahiru Thirimanne on two as the visitors chased down New Zealand's 248 all out in 47.4 overs.
"Pretty pleased with that performance," Mathews said. "They got off a brilliant start with Brendon McCullum's batting but our spinners really pulled them back by taking wickets.
"(Dilshan) got off to a start and once he got set he batted through, which is what we want from our first four batters.
"On the field we were brilliant, taking four runs outs, so it was a clinical performance by the whole team."
Dilshan was the key for the visitors, combining with fellow opener Dimuth Karunaratne (21) in a 64-run opening stand before enjoying solid partnerships with Kumar Sangakkara (38), Mahela Jayawardene (27) and Mathews that kept the scoreboard ticking over at almost a run a ball.
"It was a really good surface to bat on, with the ball coming on to the bat," said Dilshan, who also provided seven tidy overs with his offspin.
"I've really been enjoying bowling in the last six months. It was not easy to bowl on this wicket, it's really flat and not much turn, but if you put it in the right areas batsmen will take chances."
New Zealand captain McCullum had earlier blasted 12 boundaries and five sixes to score 117, his fifth one-day international century for his side, the only other bright spot in a otherwise poor performance from the hosts.
McCullum took the hosts to 158-2 in the 31st over, then New Zealand lost five wickets, four of them to run outs, for 49 runs and the captain said that had been crucial.
"Four runs outs is not good enough," McCullum said.
"We probably let a little bit of panic set in... and we have to learn the lesson from it because we were in a pretty good position and threatening a 300-plus score.
"Credit to Sri Lanka, they deserved to win."
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien; Editing by John O'Brien)
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