Their partnership was broken up by Kane Williamson, who dismissed Lyon for 33, but Voges's knock of 60 off 127 balls kept things ticking.
On the field, Neil Wagner impressed for New Zealand as he nabbed four wickets during today's play, taking his total first-innings tally to six.
Australia's tail-end scored less than 20 runs individually, but the work had already been done as the tourists posted 505 runs before going into bowl.
Pattinson also dismissed Tom Latham (39) and Henry Nicholls (2), while Josh Hazlewood prevented outgoing captain Brendon McCullum from another historic knock by sending him back to the pavilion on 25 runs.
New Zealand ended the day on 121-4, with Williamson and Corey Anderson unbeaten on 45 and nine runs respectively.
The hosts trail by 14 runs.