Taylor, who had been joined by Neil Wagner, hit his 23rd boundary to move to 199 before paddling the ball behind square for three runs to reach the milestone and prompt a standing ovation from the crowd at University Oval.
He was the 13th New Zealand batsman to score a double century in Test cricket.
Wagner attacked after tea, blasting two sixes and three boundaries before he was run out for 37, which prompted McCullum to declare about 25 minutes into the final session.
“We could have easily been bowled out for 450, which would have been a good total, but not deserved of yesterday’s performance,” Taylor said. “Those little partnerships of 50 or 60 are always valuable and I’m sure for the rest of the series, those guys all got starts and hopefully they can continue later on.”