The All Blacks trailed 16-12 until the 56th minute but their second-half dominance eventually paid off when scrumhalf Aaron Smith and replacement forward Sam Cane scored tries following a first-half score by Pumas lock Guido Petti.
Flyhalf Dan Carter kicked 16 points for New Zealand and his opposite number Nicolas Sanchez 11 for Argentina, who were looking to beat the All Blacks for the first time.
Another tournament upset possibly looked on the cards until New Zealand got their running game flowing as the hour approached and elusive scrumhalf Smith wiggled his way through to crown a series of attacks close to the Pumas line.
Cane, one of several New Zealand replacements who underlined the holders’ greater strength in depth, ran through to touch down under the posts nine minutes later.
Two previous second half chances had gone begging when wing Nehe Milner-Skudder knocked on at the line on the right and Richie McCaw later fumbled into touch on the left as New Zealand began to find the extra man outside.
New Zealand captain McCaw and centre Conrad Smith were both yellow-carded in the first half as the holders made uncharacteristic errors in the face of some fearsome Argentine tackling.
Argentina came back from three early Carter penalties to score a try after a series of mauls with Petti crashing over after 21 minutes. They had withstood All Blacks pressure for 10 minutes without conceding while flanker Pablo Matera was in the sin bin.
Sanchez’s conversion added to two penalties had Argentina changing ends 13-12 ahead after Carter’s fourth penalty success on the stroke of halftime.
New Zealand dominated possession and territory and looked dangerous with their offloads - particularly second-half replacement Sonny Bill Williams, but the Pumas' defence usually read the danger and held fast for nearly an hour.
"I guess that's what you expect first up," said McCaw. "I thought that second half was a lot more clinical.
It's been a while since our last game and we've been over here for 10 days or so, so we were itching to get out there and get started. We'll have to make a few improvements but that's the nature of rugby.
"It's a magic place to play here at Wembley, it's one of the great grounds to play at."
The 89,019 crowd, in which Argentina fans appeared to outnumber New Zealanders and certainly out-voiced them until the final quarter when the All Blacks asserted their dominance, was the biggest ever at a Rugby World Cup match, surpassing the 82,957 who watched England beat Australia in the 2003 final in Sydney’s Olympic Stadium
(Reporting by Rex Gowar)
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