Derbyshire produced a disciplined bowling performance in the afternoon, but New Zealand had comprised a 334-run lead at the close after the hosts had earlier been dismissed for 154 at the County Ground.
Neil Wagner and Bruce Martin both claimed three wickets apiece, while Doug Bracewell picked up four to bowl the hosts out 135 runs short of the tourists’ first innings total, with Wes Durston top scoring with a fluent 46.
But Derbyshire would claim three quick innings in reply, five in total in the day, with Mark Footitt again the pick of the bowlers as New Zealand closed on 199-5, a lead of 334 runs.
Speaking after the game Chesney Hughes said: "I think we did well today. We were superb at the end of the day to claim five wickets. The batting was a little disappointing as it fell away, but I think the bowlers picked it up when we came out and we had them five down for 90 which was an excellent effort.
"Hopefully they will pull out now and give us 300 to chase and I think if we can bat well and bat as we know we can bat then it will be a big confidence booster going in the next Championship game. A run chase here can do massive confidence to the guys and I am sure we will do well tomorrow."
Derbyshire resumed Day 2 on 24-1 after they had lost Chesney Hughes for nine in the final over on the opening day and the hosts could only add 11 more runs before their second wicket fell as Godleman was caught behind for 10 off Wagner.
Wayne Madsen and Durston moved the scores past 50 after 22 overs, with Madsen hitting some beautiful shots through mid-wicket, but his innings was ended on 12 as he too edged Wagner behind to reduce Derbyshire to 52-3.
Durston, joined by Dan Redfern, continued to take the attack to the New Zealand bowlers hitting some sublime shots through the covers, including 14 runs from one Mark Gillespie over as Derbyshire moved onto 88-3 from 27 overs.
But the 37-run stand was broken when Redfern was caught brilliantly by Peter Fulton at first slip off Bracewell for 10. And Bracewell would be on a hat-trick when Whiteley was caught at third slip off the very next delivery to reduce the hosts to 89-5.
Durston and new batsman Richard Johnson both looked comfortable at the crease moving Derbyshire past three figures in the 31st over, as Johnson moved down the wicket to powerfully hit Bruce Martin over mid-off for four.
But another promising partnership was broken as Martin claimed his first wicket, that of the fluent Durston who hit a well made 46 before he was stumped by sub keeper Tom Latham, as Derbyshire entered Lunch on 129-6.
And wickets continued to fall in the afternoon session as Johnson (16) went to an excellent catch from Kane Williamson at short mid-wicket, before Higginbottom went shortly after for 2 after he was caught by Watling also at mid-wicket.
Four byes moved Derbyshire past 150, but the last two wickets fell in quick concession as Burgoyne was clean bowled by Bracewell for 6 and Footitt soon followed without scoring as Derbyshire were dismissed for 154, trailing by 135 runs.
The hosts regrouped and started brilliantly with the ball taking two quick wickets to dismiss both New Zealand openers.
First Footitt (2-19) clean bowled Hamish Rutherford without scoring and then Evans (1-30) dismissed Peter Fulton for three in a carbon copy of the first dismissal, as the tourists were reduced to 9-2 inside three overs. And it would get even better for the hosts before Tea as Higginbottom (1-26) removed Guptill’s off stump to leave New Zealand 34-3 at the interval.
Williamson and Dean Brownlie put on another 26 runs before Footitt claimed his second wicket of the innings, as the latter was bowled for eight. Derbyshire continued to find regular wickets of their own as 19-year-old Burgoyne (1-59) produced a turning delivery that Williamson dragged on to reduce the tourists to 94-5.
But Watling (61*) and Tom Latham (47*) produced an excellent 105-run partnership taking New Zealand to the close on 199-5.
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