Cesc Fabregas also scored before the break and David Villa added the fifth shortly after the restart.
Spain moved top of Group A on three points, two ahead of South Africa and Iraq, who drew 0-0 earlier in the day.
The EURO 2008 winners, who are firm favorites to win the Confederations Cup, extended their unbeaten run to 33 matches.
They next face Iraq on Wednesday in Bloemfontein.
Torres Heroics
Torres needed just six minutes to break New Zealand’s resistance.
He controlled a David Villa pass on the edge of the area and curled a delightful right-foot shot into the top corner.
On 14 minutes, Albert Riera released Villa with a deft through pass on the left flank.
The Valencia striker sent in a low cross for Torres to easily convert the ball past New Zealand’s hapless keeper Glen Moss.
Three minutes later, Torres completed his hat-trick when he rose unmarked to head home Joan Capdevila’s pinpoint cross.
Fabregas heaped more misery on New Zealand in the 24th minute with an easy tap-in after the lively Capdevila cut the ball back for him.
New Zealand pushed forward afterwards in search of a consolation goal but were not able to create any clear-cut opportunities.
Villa completed the rout three minutes after the restart after capitalizing on a dreadful blunder by Andrew Boyens.
The New Zealand defender tried to clear Torres’ cross but his mis-hit kick allowed Villa to fire a low shot home from close range.