A defiant unbeaten 80 from Kane Williamson has given New Zealand a chance of saving the second Test against Sri Lanka, who were left to rue missing two gilt-edged chances to remove him.

Williamson was put down twice – the first occasion when the hosts were only one run ahead – but rode his luck to steer the Black Caps to 5-253 at the close of day three at the Basin Reserve.

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They have eked out a lead of 118 and with wicketkeeper BJ Watling (48 not out) Williamson has added 94 for the sixth wicket.

Their situation appeared parlous when skipper Brendon McCullum departed for 22 – 280 runs shy of his record-breaking innings to save the Test against India at the same ground last February.

At that stage they still needed 13 runs to make Sri Lanka bat again and when James Neesham, a century-maker in that Test, fell they were just 24 ahead.

But Williamson found a handy ally in Watling, who was the third century-maker in the great escape against India, as the home side staged a rearguard defence to ensure the match would go into a fourth day on a pitch becoming easier to bat on.

Sri Lanka, who stuck to their task admirably during the partnership, blew opportunities offered by Williamson on 29 and 60 – a tough caught and bowled chance grassed by Rangana Herath and a simple chance at deep fine leg by Nuwan Pradeep.

They may look back on them as mistakes that may cost them squaring the series.

Pradeep was again the pick of their bowlers, belying his bowling average of almost 73 coming into the match.

The 28-year-old backed up his four wickets in the first innings with another clutch, removing both openers and then Neesham to end with 3-57.

The Black Caps started the day on 0-22 and had progressed comfortably to 75 without loss before Pradeep softened up Hamish Rutherford (40) with a short ball to entice a slash to deep third man.

It was his and Tom Latham’s best partnership to date, but Latham followed 13 balls later chasing a loose one and Ross Taylor’s duck after playing the wrong line to Herath meant the hosts had shipped three wickets in just 30 deliveries.

But Williamson, on the ground where he defied South Africa’s mean acing attack for over five hours in 2012 to score an unbeaten ton, followed his first innings’ 67 with his 16th Test half-century.

He will start the fourth day 20 runs short of becoming the seventh New Zealand batsman to score nine Test tons.

-AAP