Compton was more workmanlike in his display as he ground down the Kiwi bowlers and inched his way towards his second hundred in as many matches after he posted his maiden ton in the drawn first test in Dunedin last week.
The 29-year-old reached his milestone with a beautiful cover drive from the bowling of Wagner and celebrated with enthusiasm.
Eventually, Compton succumbed to a loose drive when he was caught at first slip by Ross Taylor from the bowling of left-arm spinner Bruce Martin.
Taylor's catch was his 69th in his 45th test and he is now one behind Nathan Astle for the third-most by a New Zealander in test cricket and two behind Martin Crowe who pouched 71 in his 77-match career.
Kevin Pietersen survived a late LBW appeal by Trent Boult to finish the day unbeaten on 18.
New Zealand had begun brightly when they dismissed Alastair Cook for only 17 during the first session.
Wagner drew the England skipper into a false stroke and he spooned a catch to a grateful Peter Fulton at mid-on.
Cook made 116 in the second innings of the first test and McCullum spoke before this match about the importance of taking the English captain's wicket early.
That first-session optimism was eventually driven in to the hard Basin Reserve outfield though as England made the most of the batsman-friendly conditions for the rest of the day.
New Zealand will have to take early wickets tomorrow as they look to find a way in to the test.