Chandimal was supported well by Angelo Mathews (78no), Kamindu Mendis (51no) and Dimuth Karunaratne's 46 on Thursday.
Sri Lanka and England share the record for the most Test wins at a single venue, 25, at Galle and Lord's respectively, and now the hosts have made a great start to owning the mark outright.
Chandimal and Karunaratne combined for 122 for the second wicket until a mix-up ended with Karunaratne being run out. He hit to square leg and attempted a quick single after a misfield but was sent back by Chandimal and didn't make it.
But Chandimal remained composed, going on to score his first test ton against New Zealand and his sixth in Galle.
Only Kumar Sangakkara and Mahela Jayawardene, with seven centuries each, have scored more at the iconic ground.
Chandimal and Mathews added 97 runs for the third wicket before Glenn Phillips broke through.
Chandimal, who had been using his footwork expertly against spin, misjudged the offspinner's flight and was bowled while attempting another aggressive shot. His 116 came off 208 balls, featuring 15 boundaries.
The in-form Mendis joined Mathews and began to score with ease. Mendis finished the day unbeaten on 51 from 56 balls, laced with eight boundaries and one towering six. In the past month, he has amassed three fifties and a century.
Mathews, solid as ever, was still there, having struck six boundaries from the 166 deliveries he faced while going past 2000 Test runs in Galle in the process.
The pair have put on 85 runs for the fourth wicket at the end of a long day for the toiling New Zealand attack in hot, humid conditions. Dropped catches didn't help their mood.
Daryl Mitchell spilled chances at slip, including one each for Karunaratne and Mendis, while wicketkeeper Tom Blundell missed a stumping opportunity off Karunaratne.
Mathews was caught down the leg side, only for the dismissal to be overturned due to William O'Rourke overstepping.
"Not the day we would have liked to walk away with," Phillips said.
"A couple of catches dropped and a few other chances gone begging. Sri Lanka made us pay. We generally are a very good fielding unit and we work hard at training. It is unusual.
"You have to really appreciate the effort the bowlers put in. It was very tough out there but they kept fighting."
After winning the first Test, Sri Lanka gave a debut to offspinner Nishan Peiris and brought in allrounder Milan Ratnayake. Lahiru Kumara and Ramesh Mendis were left out, while New Zealand opted for an unchanged side.
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