Chameera took his first five-wicket bag as New Zealand slumped from 81 without loss in reply to Sri Lanka's first innings score of 292 to be 232-9 at stumps.
Doug Bracewell was not out 30 after a ninth-wicket stand of 31 with Neil Wagner (17) who was dismissed on the last ball of the day.
The 20-year-old Chameera, bowling at up to 146 kilometres per hour (90.6 mph), was used sparingly by captain Angelo Mathews, taking three for 17 in his first spell and two for 30 in his second.
In partnership with the wily 37-year-old Rangana Herath, playing his 67th Test, they took New Zealand apart when it seemed openers Tom Latham and Martin Guptill were settling in.
New Zealand lost four wickets for eight runs in four overs as Chameera claimed the scalps of Latham, Kane Williamson and Ross Taylor while Herath removed Guptill