The unlucky Doug Bracewell took the last wicket when he caught and bowled Suranga Lakmal for 23 to help dismissed the touring side for 282.
Bracewell had two catches dropped off his bowling during the course of the match so there was some reward for all his hard work.
His team-mate, Neil Wagner, struck the first blow when he baffled Angelo Mathews and bowled the captain for 25 during the morning session.
Dinesh Chandimal was out shouldering arms 12 minutes later and from there Sri Lanka always seemed destined for defeat.
Sri Lanka resumed the day on 109 for three and at the break is 224 for six. They still need 181 runs to win but that seems unlikely given key batsmen
Angelo Mathews (25) and Dinesh Chandimal (58) have been dismissed.
The touring side resisted the Black Caps for 20 overs before the captain Mathews had one of those moments best described as a brain explosion.
He was never that comfortable with Neil Wagner's leg stump line and made a complete hash of the ball that got him out. He tried to pad it away
but only managed to get himself hopelessly out of position.
The ball struck his leading pad and the deflection cannoned into middle stump.
Twelve minutes later Chandimal made a baffling decision to shoulder arms to a straight delivery from left-arm spinner Mitchell Santner and was
given out lbw. Even the review could not save him.
And just before the break Kithuruwan Vithanage was trapped lbw for 38 by Tim Southee with the new ball.
Sri Lanka had resumed on 109-3 and needed to score 296 further runs from 98 overs to achieve the fourth-highest successful run chase in tests.
Chandimal had resumed on 31, while Mathews joined his wicketkeeper today after rain and hail halted play yesterday before he could make it to the crease.
Neither looked troubled on the benign pitch and with Trent Boult and Tim Southee not able to get the older ball to reverse, captain Brendon McCullum was forced to go into a holding pattern and attempt to force an error rather than attack the batsmen.
Chandimal brought up his 10th test half-century when he pulled a short ball from Doug Bracewell down to fine leg for a single, though he was not able to fully capitalise as both he and his captain fell shortly after the drinks break.
Wagner also trapped Siriwardana in front for one when the ball hit his back leg on the full, though the batsman was recalled after successfully reviewing the decision.
The second test is in Hamilton and starts on Friday.
- additional reporting Reuters
