Put in to bat by Brendon McCullum, England lost captain Alastair Cook early on but any worries there could be a repeat of what happened in the drawn first Test, where they were dismissed for just 167, were methodically stamped out by Trott (121no) and Nick Compton (100) in a second-wicket stand of 210.
Trott told Sky Sports 1: "We're very happy. Being put in it was important we came out and put on a better show than the first innings of the last game.
"I was a bit disappointed the way I got out in Dunedin, two soft dismissals, and I was really up for today."
The way the day panned out left McCullum with egg on his face somewhat after he chose to field upon winning the toss, but England were planning to do the same.
Having inspected the pitch in the morning, though, Trott had a feeling it might be a good toss to lose.
"I said to Cook I won't be too unhappy if we lose the toss and bat," he said. "It was a good surface."
Opener Compton was the first to his half-century at a marginally quicker tempo than Trott before he retreated into a sheet-anchor role.
His second 50 runs took 111 balls, eight more than his first, while Trott accelerated more conventionally to reach three figures from 174 deliveries.
"We both had ebbs and flows where we scored quickly and then a bit slowly," Trott said. "That's Test cricket - you have to earn the right to score your runs."