McCullum and Taylor then crushed the tourists' spirits with their partnership, which began just before the break for tea.
Taylor took only 66 balls to reach his half century and McCullum, under pressure to regain his form after scoring just 92 runs in eight innings in his last four tests, reached his from 58 balls with nine fours.
The pair raised their century partnership in 86 minutes from 125 balls as McCullum, who scored 60 of those runs, inched closer to Taylor's run total. He finally matched Taylor at 94 after they had raised a 150 partnership from 183 balls in 120 minutes at a strike rate of 0.81.
McCullum reached his century just before the arrival of the second new ball, after batting for 128 minutes, facing 101 balls and hitting 13 fours and three sixes. Taylor followed soon after, reaching his ninth test century from 150 balls in 208 minutes.
Taylor had a few close calls in the 90s - an appeal for caught behind which required the scrutiny of the television umpire and an inside edge which passed perilously close to his off stump. But he reached his century with his 13th boundary just before stumps.
"I think I was fighting a few demons at the start of the day," he said. "I wasn't feeling the greatest but it's nice when you can push through those barriers and come through the other side with some well-earned runs."
New Zealand's dominating performance may have Sammy rethinking his decision to bowl after winning the toss. But after his squad lost its last test series in India on dry and turning wickets, he couldn't help but be dazzled by the green colour of the pitch at the University Oval.
"I've never seen a pitch with so much grass," he said as he announced his decision to bowl.
The tourists' lacklustre performance in the first session, however, suggested they were relying too much on the pitch to do the work of the bowlers.
AP