New Zealand bowled out Sri Lanka for 282 to win the first Test by 122 runs in Dunedin.
Sri Lanka resumed on day five on 109 for three, needing a further 296 to win or more realistically to bat all day without losing their remaining seven wickets for a draw.
The lesser goal still proved comfortably beyond them as they subsided midway through the afternoon session, Tim Southee finishing with three wickets and six in the match.
It looked encouraging for the tourists as Dinesh Chandimal and Angelo Mathews batted through the first hour, the former reaching a good half-century in the process.
But the breakthrough came when Neil Wagner set Mathews up with his persistent bouncer attack before firing in a full, straight ball which took out middle stump - and t here was no further addition to the score when Chandimal fell lbw to Mitchell Santner for 58, from 132 balls with 11 fours.
Kithuruwan Vithanage and Milinda Siriwardene put on 48 for the sixth wicket, though the stand occupied only 8.1 overs as Vithanage hit a run-a-ball 38 with six fours and a six before Southee's lbw appeal was upheld by the decision review system.
Rangana Herath and Siriwardene fell in successive Trent Boult overs and Santner bowled Dushmantha Chameera, who missed with a wild slog, to leave just one wicket to fall.
Santner prevented a Lakmal six with a superb dive to catch the ball and flip it back inside the rope, and though the tail-ender hit Doug Bracewell for four to reach a Test-best 23 he popped up a return catch to the same bowler next ball.
New Zealand captain Brendon McCullum told Sky Sports 3: "We had to work pretty hard to get the 20 wickets. It's a very professional performance and one we're very pleased with.
"You're always a little concerned but you've got to keep a positive face and you know when you've got a guy like Neil Wagner, who can bowl long spells and hostile spells, you're always in the game."
Martin Guptill was named man of the match after his 156 in New Zealand's first innings, while Tom Latham made 109 not out in the second before an aggressive McCullum declaration which caught many observers by surprise.
The skipper admitted the weather played a part in his thinking - rain and hail delayed day four several times - and also pointed to his side's established approach in recent years.
"Sometimes you've got to risk losing to win it," he said. "We needed enough time to bowl Sri Lanka out and with the weather possibly in play again today, we needed that time.
"The way Martin Guptill and Tom Latham started, we got off to a four-an-over start on the first morning and to be able to put on 400 on the first day - yeah, we probably lost a couple more wickets that we'd have liked, but it enabled us to advance the game."
The teams meet again in Hamilton from December 18, with that second Test followed by five one-day internationals and two Twenty20 matches.