The 26-year-old led the way with a patient half-century before the tourists declared their first innings close on 261-9 to give their bowlers a run out after day one was washed out on Thursday.
In reply, the home side reached 65-1 off 24 overs before stumps, as England all-rounder Moeen Ali followed up figures of 2-35 by scoring an unbeaten 20 after Richard Oliver fell for 30.
Moeen ??? included in England???s squad to face the Black Caps in next week???s first Test at Lord???s ??? ended Rutherford???s 140-ball knock when the number three was smartly stumped by Ben Cox.
No other New Zealand batsman made it past 50 ??? number nine Doug Bracewell coming closest with a breezy 43 that featured six fours and one six.
Opener Martin Guptill contributed 35 at the top of the innings but wickets fell regularly as the home attack chipped away, Charlie Morris finishing with 2-32 and Ross Whitely collecting 2-16.
At 191-8 a target of over 250 looked unlikely but New Zealand snuck past that mark as Bracewell shared a ninth-wicket stand of 70 with Neil Wagner.
The home side lost just one wicket in their reply ??? that of Oliver ??? caught by Guptill at third slip off Wagner.