New Zealand were 96 for six in reply to England's first innings 364, a deficit of 268, and still 69 runs short of avoiding the follow-on.
Fast bowler James Anderson had taken all the New Zealand wickets to fall so far with the 25-year-old Lancashire quick's figures of six for 42 his best in Test cricket.
Gareth Hopkins, on his Test debut, was 11 not out and New Zealand captain Daniel Vettori unbeaten on three.
The umpires announced an early lunch would be taken at 12.40pm local time (1140GMT) with a view to resuming at 1.20pm (1220GMT).
England lead the series 1-0.