Kane Williamson was hailed as "world class" after New Zealand's record Test run-scorer orchestrated a dramatic last-ball win over Sri Lanka on a rain-disrupted final day in Christchurch on Monday.

The thrilling triumph at the Hagley Oval scuppered Sri Lanka's chances of making the World Test Championship final, handing the spot to India.

Having lost eight wickets and on a day limited to 53 overs, skipper Tim Southee paid tribute to his star batsman Williamson. The former captain finished 121 not out and ran a bye off the final delivery of the match in a remarkable conclusion, to go with New Zealand's one-run victory over England a fortnight ago.

"Seeing how calm he is out in the middle keeps us calm as well," Southee said as New Zealand celebrated another famous, nail-biting win.

Visiting captain Dimuth Karunaratne said that fielding errors let his side down, particularly dropping the talisman Williamson on 33.

When rain wiped out the first two sessions on the fifth day, the umpires ruled there would be a minimum of 53 overs played in the evening, which meant New Zealand would have to average 4.85 an over.

After a steady but slow start which saw the hosts at 90-3, Williamson and Mitchell picked up the pace.

The 31-year-old Mitchell, a late arrival on the international stage, contributed 81 to lift his average to a phenomenal 59.04 from 26 innings.

In a match of see-sawing fortunes, Sri Lanka had the upper hand on the opening two days before a first-innings century from Mitchell and a swashbuckling 72 from Matt Henry -- the last 60 from only 35 deliveries -- swung the game in New Zealand's favour.

Sri Lanka fought their way back into contention on the fourth day with a defiant 115 from Angelo Mathews, who built partnerships of 105 for the fifth wicket with Dinesh Chandimal and then 60 with Dhananjaya de Silva.

The second Test starts in Wellington on Friday.