The European champions stretched their unbeaten run to 33 matches, further goals from Cesc Fabregras and David Villa putting them firmly on top of Group A after hosts South Africa and Iraq drew 0-0 in the opening game in Johannesburg.
The match was virtually all over as a contest after only six minutes when Torres sent in a curling shot from the edge of the penalty area well out of the reach of New Zealand keeper Glen Moss.
The Oceania champions were undone again eight minutes later when Albert Riera and David Villa combined on the left to create the second for Torres.
Villa provided the sweetest cross and Torres steered the ball home with a well-taken shot despite being surrounded by defenders.
Three minutes later Torres completed his hat-trick with a powerful header from Juan Capdevila's cross and Fabregas's close-range finish assured Spain of their 13th successive win and 11th straight victory under coach Vicente Del Bosque.
CREATE CHANCES
Spain, who have not lost since Romania beat them 1-0 in a friendly in Cadiz in 2006, continued to create chances with Riera thundering in a shot which Moss did well to save.
Things got no better for New Zealand after halftime when defender Andy Boyens made a mess of the simplest cross from Torres, allowing the ball to run to Villa who had scored a hat-trick in Spain's 6-0 friendly win over Azerbaijan last week.
That was Villa's 29th goal in 45 internationals, putting him level with Fernando Hierro as Spain's joint-second highest scorer, 15 behind Raul's record haul of 44.
Underlying everything was Spain's slick passing and movement which provided a treat for the disappointingly sparse but enthusiastic crowd in the 44,000 capacity stadium.
