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Half centuries from Ross Taylor (90), Colin Munro (87) and James Neesham (64) helped push New Zealand past the magical 300 mark.
Some skittish running between the wickets stopped NZ from posting anything higher, with four runouts marring an otherwise impressive batting display.
All three half-century-makers, along with Tim Seifert, fell victim to a combination of good Sri Lankan fielding and poor calling.
A 112-run-partnership between Ross Taylor and Colin Munro dug the kiwis out of early trouble, having lost both Martin Guptill and Kane Williamson early.
More big hitting at the death from James Neesham elevated the total, with his 64 coming off just 37 balls, including three sixes and five fours.
Sri Lanka will hope to put in another strong batting performance when play resumes, after they made 326 in a losing cause at the same ground on Thursday.