Kamindu Mendis century propels Sri Lanka past 500 against Kiwis
He was an unbeaten 135 at the second break alongside Kusal Mendis, who became the fourth batsman to make a half-century in the innings with his 70, in the third century-plus partnership of the match so far.
The 25-year-old resumed from overnight after making his world record eighth consecutive fifty from eight Test appearances since his debut against Australia at the same venue two years ago.
He was an unbeaten 135 at the second break alongside Kusal Mendis, who became the fourth batsman to make a half-century in the innings with his 70, in the third century-plus partnership of the match so far.
Kamindu's five centuries from 13 innings makes him third-fastest to the milestone, tied with Australian great Donald Bradman and George Headley of the West Indies.
Kamindu was also the only batsman from either team to make a century in the first Test.
He has been in excellent form this year and was also Sri Lanka's highest run-scorer in their last two series against Bangladesh and England.
Kamindu's overnight partner Angelo Mathews departed for 88 when Glen Phillips got him caught at square leg by rookie quick Will O'Rourke.
Phillips then sent back Dhananjaya de Silva for 44 when the skipper swept a delivery into the gloves of wicketkeeper Tom Blundell.
It was Phillips's third wicket for the innings after he bowled Dinesh Chandimal 116 on the last session of the opening day.
O'Rourke had impressed in the first Test with his second five-wicket haul in three matches, but has toiled without result in the innings so far, conceding 81 runs without reward.
Sri Lanka won the opening match of the two-Test series by 63 runs and are eyeing their first Test series win against the Kiwis since 2009.
Friday was the first time Sri Lanka surpassed 500 against New Zealand from 40 matches.
New Zealand have not won any of their five previous Tests at Galle.