He then guided them to within the sight of victory alongside Nathan McCullum (25 not out) in a 60-run stand, before he was dismissed with 10 runs needed as the hosts made 219-7 in 43 overs, chasing Sri Lanka's 218-9.
"I thought it was a really good performance from us," said New Zealand captain Brendon McCullum, who got his side's run chase off to a blistering start with a 19-ball half century.
"We were outstanding with the ball and in the field but with the bat we made ourselves fight pretty hard... and Corey, under pressure, really stepped up nicely and got the job done.
"We need to get better, but overall not a bad performance."
Mahela Jayawardene had anchored Sri Lanka's innings with his 18th one-day century, before their spinners Sachithra Senanayake and Tillakaratne Dilshan showed how dangerous they could be in the World Cup as they put the middle order under pressure.
Sri Lanka's innings had been built around Jayawardene, though the 37-year-old did get some middle order assistance from Lahiru Thirimanne (23) and Jeevan Mendis (23) in partnerships worth 118 runs.
Jayawardene appeared effortless working the ball into space, though he did tempt fate with several short singles that would, had the fielders' throw at the stumps hit, have run him out comfortably.
The veteran, who will retire after the World Cup, was dismissed for 104, which included 12 boundaries and a six.
New Zealand's Mitchell McClenaghan took three wickets in the 47th over, and finished with figures of 4-36, to ensure there were no late blasts from the tail.
"I thought we were about 30 or 40 runs short on that wicket," Sri Lanka captain Angelo Mathews said.
"I am proud of the way we fought on the field and particularly the way that Sachithra, (Nuwan) Kulasakera and Dilshan bowled. They're our main bowlers and we needed them to come back hard."
The second game is in Hamilton on Jan. 15.
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)
Share
