At dinner, Martin Guptill was on 10 with Tom Latham not out 10.
Australia were all out for 224 to take a first-innings lead of 22 runs.
Australia got the benefit of a controversial review before Nathan Lyon had scored and went on to overhaul the Kiwi total of 202.
Lyon went on to score 34 in a record Australian trans-Tasman ninth-wicket stand of 74 with Peter Nevill, who finished with 66 while injured Mitchell Starc hit out for an unbeaten 24.