Bangladesh fell apart in the face of Neil Wagner's short-ball barrage and were all out for 209.
Sri Lanka resumed Sunday on 231 for six before being bundled out for 236.
After rain ensured a drawn first Test in Wellington, a win in the Christchurch decider would give New Zealand a fourth consecutive series win.
New Zealand pulled off a thrilling four-run win over Pakistan to take a 1-0 lead in the three-Test series.
The second Test draw in Christchurch gave New Zealand the series 1-0 after they won the first Test by an innings and 49 runs.
A brutal spell from Neil Wagner, including three wickets and a broken arm, led New Zealand to a comprehensive victory over the West Indies in Hamilton on Tuesday.
Neil Wagner claimed seven for 39 as the West Indies crumbled to be all out for 134 in a first innings that lasted a mere 45.4 overs.
Mominul Haque and Tamim Iqbal plundered the New Zealand attack to have Bangladesh 154-3 at stumps on a rain-disrupted opening day of the first Test.
Tim Southee captured three quick wickets to put New Zealand in a commanding position in the second Test against Pakistan.
Pakistan lost six wickets in the final session at Hagley Oval to be 129-7 at stumps against New Zealand, ahead by only 62 runs with two days remaining
Mumbai, who started on their overnight score of 29 for one, were 431/5 at stumps on Day 2 in reply to New Zealand' first innings total of 324/7d. Rohit Sharma, who has managed to retain his place in India's Test squad, scored just 18
South Africa struggled to 236 for eight at the close of play after deciding to bat in overcast conditions, with the floodlights on for most of the day
South Africa, the top-ranked Test team before defeats against India and England, return to the five-day format at Kingsmead on Friday against Kane Williamson-led New Zealand, who showed some brilliant form in Zimbabwe
New Zealand won the series 2-0 after bowling Zimbabwe out for 132 in their second innings, though the home side were hampered by poor umpiring decisions
Sean Williams hit the fastest Test century by a Zimbabwean, but his knock was not enough to prevent New Zealand from clinching an innings victory
Neil Wagner helped New Zealand bowl out Zimbabwe for a meagre 164 to then put on 32 for no loss at the end of Day 1 in the first Test.
Australia won the final Test at Christchurch by seven wickets to sweep the series 2-0 and secure the world number one ranking in Tests.
Neil Wagner bowled a bouncer which at Steven Smith and the Australian captain suffered a blow to the head during the second day of the second Test in Christchurch.