A classy century from Angelo Mathews revived Sri Lanka's fortunes and set them up for a challenging total as they reached 251 for five at tea on day four of the first Test against New Zealand.

The tourists held a 233-run lead at Christchurch's Hagley Oval where the highest fourth innings score is New Zealand's 256 for eight in a drawn Test against England in 2018.

Mathews was unbeaten on 108, his 14th Test hundred, with Dhananjaya De Silva on 25.

It has been a near chanceless innings from the right-hander who brought up his century with a backfoot drive through cover off a short Blair Tickner delivery.

It was one of only 11 boundaries from the 229 deliveries Mathews has faced.

Dinesh Chandimal, who shared in a 105-run stand with Mathews for the fifth wicket, posted 42 before he was bowled by Tim Southee.

Black Caps skipper Southee had fired a series of outswingers before catching Chandimal off-guard with one that swung in and found the gap between bat and pad.

The only other wicket claimed by New Zealand as they toiled on a hot Sunday was nightwatchman Prabath Jayasuriya who fell early for six.

Sri Lanka, who were 18 runs behind on the first innings, would like to set the hosts a target of at least 275-300 on a pitch that continues to offer assistance to the quick bowlers, their assistant coach said after the close of play on Saturday.

They must win in Christchurch and again in the second Test in Wellington to stay in contention to make the World Test Championship final.

Sri Lanka resumed at 83 for three on Sunday, with Mathews and Jayasuriya adding 12 in seven overs before Tickner had the nightwatchman caught behind for six.

Tickner, in only his second Test, took the first four second-innings wickets to fall and faces an extra workload with veteran seamer Neil Wagner ruled out of the attack.

Wagner has a back issue and has been absent since he left the field late the previous day.

All-rounder Daryl Mitchell, who scored a century for New Zealand with the bat, took on Wagner's traditional bouncer role but without success.

Mathews, while risk-free for most of his stay in the middle, did lash out to bring up his half-century.

But luck was on his side as the ball was top-edged to the boundary.