New Zealand were flailing at 22-2 and trailing by 580 on Friday against a dominant Sri Lankan batting attack that saw middle-order maestro Kamindu Mendis reach 1,000 runs from just eight Test appearances.
Sri Lanka declared at 602-5 shortly before stumps on day two in Galle after a 200-run partnership between Kamindu and Kusal Mendis -- the third century-plus stand of the innings.
The tourists then lost their openers inside nine overs, with Tom Latham caught on the fifth ball of the innings for two and Devon Conway dismissed for nine.
Kane Williamson (six) and Ajaz Patel (nought) will resume on Saturday.
Kamindu reached the 1,000-run milestone in 13 innings played since his debut at the same ground two years ago, equalling the record of Australian great Don Bradman.
Only two others -- England's Herbert Sutcliffe and Everton Weekes of the West Indies -- have surpassed him, both reaching the landmark in 12 innings.
"Kamindu Mendis, obviously he has just taken off," all-rounder and former captain Angelo Mathews told reporters.
"He doesn't get rattled and plays one ball at a time," he added. "He is quite amazing."
Kamindu, a 25-year-old Galle native, made an unbeaten 182 before the declaration alongside Kusal on 106.
His five centuries from 13 innings also made him third-fastest to that record, tied with Bradman and the West Indies' George Headley.
The left-hander 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 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 for 116 in 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 toiled without result in Sri Lanka's innings, conceding 81 runs without reward.
"The surface is different to first Test," New Zealand batting coach Luke Ronchi said.
"We missed some chances as well... in the subcontinent it's difficult if you give the batters a chance."
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.