Anderson scored 75, McCullum 65 while Kane Williamson chipped in with 57 as the Kiwis gave the Lankans a 332 run target to chase.
For Sri Lanka, leg spinner Jeevan Mendis took two for five off two overs and Suranga Lakmal two for 62. Kulasekara and Herath too picked up one wicket each.
Earlier, the 2015 edition of International Cricket Council's (ICC) World Cup kicked off in Christchurch, New Zealand with Sri Lanka winning the toss and putting the Kiwis into bat first.
Sri Lanka captain Angelo Mathews, who prefers batting first, opted to bowl first because he could not overlook a wicket "that looks fresh" and the sky overcast.
Soon after the toss, however, covers had to be brought on at the Hagley Oval as a light shower swept the field. But players were soon back out on the field to get the tournament underway.
New Zealand captain Brendon McCullum, who would have preferred to bowl first, said batting was not a setback.
"The wicket looks good, but we have batted here first in the past with success."
Sri Lanka omitted Dinesh Chandimal, Thisara Perera, Dushmantha Chameera and Sachithra Senanayake from their side while New Zealand left out Kyle Mills, Mitchell McClenaghan, Tom Latham and Nathan McCullum.
Teams
New Zealand
Brendon McCullum (capt), Trent Boult, Grant Elliott, Martin Guptill, Adam Milne, Daniel Vettori, Kane Williamson, Corey Anderson, Tim Southee, Luke Ronchi (wkt), Ross Taylor
Sri Lanka
Angelo Mathews (capt), Tillakaratne Dilshan, Kumar Sangakkara (wkt), Mahela Jayawardene, Lahiru Thirimanne, Dimuth Karunaratne, Jeevan Mendis, Suranga Lakmal, Lasith Malinga, Nuwan Kulasekara, Rangana Herath
Umpires: Nigel Llong (ENG), Marais Erasmus (RSA)
TV umpire: S. Ravi (IND)
Match referee: David Boon (AUS)
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