The tourists were under pressure to perform having collapsed in dramatic fashion during their first innings of the first Test, but responded by hitting 267-2 after being put into bat.
Trott, who scored an unbeaten 121 on the opening day, is delighted with the way his side conducted themselves from the off.
"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," Trott told Sky Sports News.
"I was a bit disappointed the way I got out in Dunedin, two soft dismissals, and I was really up for today."
Trott formed a 210-run stand with Nick Compton (100) in Dunedin.