This victory, Sri Lanka's most dominant over the Kiwis, also marks their first win against New Zealand in 15 years.
The hero of the games, left-arm spinner Prabath Jayasuriya, was named player of the series after a masterful performance, claiming 18 wickets across the two matches.
Meanwhile, Kamindu Mendis took home man-of-the-match honours for his unbeaten 182, anchoring Sri Lanka's colossal total of 5-602 dec.
With this knock, Mendis etched his name in history, joining the great Sir Don Bradman as the third joint-fastest player to reach 1000 Test runs.
Jayasuriya, who took nine wickets in the first Test, was at his best again, snaring another nine in the second as New Zealand's batters struggled to cope with Sri Lanka's spin-heavy attack. Debutant Nishan Peiris was the perfect foil, chipping in with nine wickets of his own, including a five-wicket haul in the second innings.
Nishan Peiris celebrates the wicket of Mitchell Santner in Galle. (AP PHOTO)
"Nishan was brilliant," Sri Lanka captain Dhananjaya de Silva said of the debutant offspinner.
"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."
New Zealand's woes began early, bundled out for a paltry 88 in their first dig. Forced to follow on, the Kiwis showed more fight in their second innings, posting 360 – their highest total of the tour and in Galle – but it was too little, too late.
Tom Blundell, Glenn Phillips and Mitchell Santner all contributed half-centuries in the second innings, but the tourists needed far more to challenge Sri Lanka's dominance.
Resuming at 5-199, the tourists lost three wickets before lunch on the fourth day. Despite Sri Lanka's fielding lapses, which saw three catches dropped, they eventually cleaned up after lunch. Jayasuriya removed Ajaz Patel and Peiris took the final scalp of Santner, stumped by Kusal Mendis, sealing the series win for Sri Lanka.
"It's very tough to be on the wrong side this week," Kiwi Tim Southee said.
"But it's a tough place to come for a foreign team, and Sri Lanka played some great cricket."
With this victory, Sri Lanka have now won three consecutive Test matches and bolstered their hopes of qualifying for the ICC World Test Championship final at Lord's next June.
With Reuters.
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