Dane Hutchinson offered respite for the Firebirds, securing a hat-trick for his maiden first-class five-wicket bag. The visitors were 206-4 at the close, a lead of 44.
Of the other Black Caps, Mitchell Santner made 33 and has 0-46 across both innings, and new-ball partnership Tim Southee and Trent Boult have match figures of 6-99 from 29 overs and 2-107 off 28.2 overs respectively. Luke Ronchi made 115 in Wellington's first innings.
Auckland have the advantage over Canterbury at Eden Park outer oval, with the visitors reaching 264-5 in their second innings, a lead of 97. Leo Carter top scored with 79 while Andrew Ellis helped reduce Auckland to 316 with 3-54.
Of the other test players, Canterbury's Tom Latham made 18 and 21 and Matt Henry made 35 and took 2-76 from 26 overs.
New Zealand A dominated the opening day of their four-day match against Sri Lanka A yesterday, posting 336-5.
Jeet Raval (152) and Dean Brownlie (68) combined for an opening stand of 153 and Henry Nicholls continued his form, reaching 67 not out at stumps.
Elsewhere, New Zealand captain Brendon McCullum is expected to return home over the weekend after delivering testimony at the Chris Cairns perjury trial taking place in London.