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Neesham hit five sixes, a two and a single in an over from Thisara Perera that included a no-ball as he made 47 not out from 13 balls in New Zealand's score of 371-7 at Bay Oval.
The ODI record for the fastest 50 is 16 balls by South Africa's AB de Villiers.
Opener Martin Guptill top-scored for the home side with 138 from 139 deliveries, while skipper Kane Williamson (76) and Ross Taylor (54) also made useful contributions.
Perera finished with figures of 2-80 off his 10 overs.
The Black Caps are favourites for the encounter - since their last one-dayer in New Zealand three years ago, Sri Lanka have won just 17 of their 59 ODIs, with seven of those victories coming against Zimbabwe and Ireland. They have also won just three of their last 11 ODIs in New Zealand.
NZ: Martin Guptill, Colin Munro, Kane Williamson, Ross Taylor, Henry Nicholls, Tim Seifert, Jimmy Neesham, Matt Henry, Ish Sodhi, Trent Boult, Lockie Ferguson.
- additional reporting NZME