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Ian Bell (127) anchored the England's innings with a patient and undefeated century.
It was a solid dress rehearsal for the upcoming test series. The gritty right-hander raised the milestone with a lovely cover drive then celebrated with a late flurry of boundaries off the bowling of both Neil Wagner and Mark Gillespie. The latter, though, had a very confident appeal for caught behind turned down when Bell was on 118.
From New Zealand's perspective, Neesham was the star.
He ripped out three quick wickets, including the prized scalps of Kevin Pietersen and Jonathan Trott as the tourists slumped to 81 for three.
Neesham's opening seven over spell netted three wickets for 30 runs, and when Wagner nicked out Alastair Cook for 60 after the lunch break, England's innings was delicately poised at 124 for four.
But Bell and Joe Root rallied, added 97 for the fifth-wicket.
Root, arguably, was the most impressive of the English batsmen on display. He played with comfort from the back foot and punched several drives through the covers. But in sight of a half century, he inexplicably missed a straight delivery from part-timer Carl Cachopa.
Bell was resolute throughout his innings and his partnership with Root rescued what was shaping as a mediocre afternoon session for the visitors.
Wicketkeeper-batsman Matt Prior took advantage of a tiring New Zealand XI attack, slapping a rapid 41 from 43 deliveries before he whacked a cut shot straight to Jeetan Patel, with Neesham celebrating a fourth wicket.
The 22-year-old gave a fine account of himself. While either Wagner or Gillespie are expected to be added to the test squad for the first test in Dunedin next month, Neesham certainly did his prospects no harm, finishing with four for 65 from 17 overs.
He got the ball to straighten off the seam just enough to unsettle England's top order and he is bound to cherish dominating an out-of-sorts Pietersen.
The classy right-hander slashed an edge which provincial team-mate Hamish Rutherford hauled in with a nicely timed leap in the slips.
Otago under-19 player Michael Rae came on as a sub fielder and took a simple catch late in the day to help dismiss Chris Woakes.