Namibia gave the two-time defending champions a first-half fright, before the All Blacks sealed a clinical 71-9 pool win at the Rugby World Cup.
A series of early penalties saw the tournament's lowest-ranked side trailling the world No.1 by just one point after half an hour, with NZ prop Nepo Laulala dispatched to the sin bin for making contact with the head in a tackle.
But New Zealand were able to steady the ship and secure a four-try bonus point by halftime, then ran away for their plucky opponents over the second half to record their third pool win in Japan.
Namibia struck first, with an angle penalty, after Anton Lienert-Brown was penalised at the breakdown.
But Jordie Barrett, making his appearance as an international first-five, showed his class with his first attacking opportunity, placing a perfectly weighted kick across field for Sevu Reece to score the first try.
Lienert-Brown atoned for his earlier indiscretion, running off Ardie Savea's shoulder and evading the last defenders on a 20m run to the line.
The Africans frustrated their higher-rated opponents for long periods, breaking the line through lock PJ Van Lill. They closed the margin to 10-9 with two more penalties from halfback Damian Stevens and then enjoyed a numerical advantage, when Laulala was dispatched to the sidelines.
But Laulala's front-row replacement, Angus Ta'avao, burrowed over beside the posts to extend the lead and as a series of penalties extended the first half, Ben Smith secured the bonus point and a 24-9 advantage at the break.
Returning from two months' injury break, lock Brodie Retallick lasted 30 energetic minutes, before he was subbed out, as planned.
Within two minutes of the restart, Joe Moody added to the try tally and the rout was on.
Barrett made a clean break up the middle and popped up again to send Lienert-Brown in for his second - probably the best of the night. Reece and Smith also secured a brace of tries each for the night.
But they were again reduced to 14 men for the final 10 minutes, when replacement prop Ofa Tuungafasi made head contact in a tackle - an identical offence to Laulala.
Even a man short, the All Blacks managed to produced a miraculous try for TJ Perenara, who replaced Barrett at first-five for the final 10 minutes. He began the move and then took a behind-the-back final pass from Brad Weber to dive across in the corner.
Last time these two teams met, New Zealand ran out 58-14 winners in pool play at the last World Cup, so this represented an improved display on the scoreboard at least. It also represented the highest score of this year's tournament, beating their 63-0 romp over Canada midweek.
With one preliminary game remaining, the All Blacks still need victory over Italy next Saturday to secure a quarter-final berth, but that would also be enough to finish top of the pool.
New Zealand 71 (Reece 2, Lienert-Brown 2, B Smith 2, Ta'avao, Moody, Whitelock & J Barrett, Perenara tries; Barrett 8 conversions) Namibia 9 (Stephens three penalties)
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