Bundled out for 88 in their meek reply to the home side's mammoth 602-5 declared, New Zealand mustered an improved display - 360 all out - in the second innings before succumbing to their heaviest defeat by Sri Lanka.
Glenn Phillips (78), Mitchell Santner (67), Devon Conway (61) and Tom Blundell (60) made half-centuries but New Zealand, who were made to follow on, could not make Sri Lanka bat again.
Sri Lanka moved to third place - behind India and Australia - in the World Test Championship (WTC) standings, while 2021 champions New Zealand slipped to seventh.
New Zealand lost Blundell early after resuming day four on 119-5, when the batter fluffed his reverse sweep against spinner Nishan Peiris (6-170).
Their lower order, however, put up a spirited fight despite the overall hopelessness surrounding their innings.
Phillip raised 64 with Santner before holing out, giving Peiris his maiden five-wicket haul.
Santner raised 53 runs with Ajaz Patel (22) and was the last New Zealand batter to fall, stumped off the bowling of Peiris, who finished with a match haul of nine wickets in his memorable debut test.
Kamindu Mendis, whose unbeaten 182 powered Sri Lanka to a massive total in the first innings, was adjudged player of the match.
Left-arm spinner Jayasuriya bagged the Player of the Series award for finishing the series with 18 wickets.
"Nishan was brilliant," Sri Lanka captain Dhananjaya de Silva said of the debutant off-spinner.
"He was doing well in the domestic area. He showed that he has the control and that he can bowl long spells and get the wickets."
De Silva also felt rejigging the batting order, getting Dinesh Chandimal at number three and Kamindu at number five, worked well for them.
"Kamindu at five can play the long innings and I can finish the game at number six," he said.
New Zealand captain Tim Southee had no hesitation in admitting they had been thoroughly outplayed in Sri Lanka.
"It's very tough to be on the wrong side this week," Southee said.
"But it's a tough place to come for a foreign team, and Sri Lanka played some great cricket."
