After scoring just one goal in the first quarter, the Kiwi side flipped the switch and put four goals in 11 minutes past the Brazilians in the second, effectively ending the game as a contest.
Striker Nick Wilson was in devastating form with four goals while Shay Neal, Simon Child, Kane Russell, Stephen Jenness and Nic Woods added to the tally.
The result was vital for their medal hopes, keeping them in contention going into their final pool match against the highly-rated Belgium.
Head coach Colin Batch said it was pleasing to come and get the result required to stay in the hunt at the Olympics.
"We're very pleased with the win, it was a crucial match that we needed three points from so this puts us back in the tournament," he said.
"We didn't set ourselves a margin but it was nice to win by nine, that could prove important if goal differential comes into play."
New Zealand opened the scoring in the 14th minute when Wilson ran onto an aerial defensive deflection into the circle and calmly guided the ball past the goalkeeper.
Four minutes later it was Wilson on the score sheet again after receiving a nice pass at the top of the circle from Hugo Inglis and smashing home on his forehand.
The Kiwis went out by three goals in the 20th minute with a perfect crash ball across the face of goal from Child finding Neal at fill dive to deflect in on his reverse stick.
Child scored one of his own five minutes out from halftime with a solo run into the circle before hammering past the keeper on the half volley.
Defender Russell sent New Zealand into the break with a 5-0 lead after rocketing a drag flick into the side of the net from his side's second penalty corner of the game.
The Kiwis kept all the momentum after the break and Wilson picked up another two goals in the 33rd and 40th minutes to extend his personal tally to four.
Striker Stephen Jenness scored New Zealand's eighth goal just out from three quarter time before Nic Woods delivered the final blow with a powerful drag flick from a 58th minute penalty corner.
