A sloppy first 50 minutes on a damp field, in which New Zealand conceded penalties and free kicks while Argentina frittered away hard-won possession, saw the All Blacks leading 14-12 but hardly feeling in danger.
The Pumas, who have yet to beat New Zealand, failed to threaten a try before 40,000 fans and could stay with the visitors only in scrums, and on the scoreboard through penalty kicks. But even by the end, New Zealand's scrum was untroubled.
New Zealand finally broke open the match with tries in the 52nd and 56th minutes featuring inside center Ma'a Nonu, leaving the Pumas behind at 26-12. The All Blacks then spent most of the last quarter desperately seeking their fourth try for a bonus point, and had to wait until the last minute to secure it.
Rain stopped before the match but left the track and ball greasy. Only one try was scored in the first half, in the 23rd minute, when Read forced Pumas flyhalf Nicolas Sanchez to forget a dropped goal attempt and send up a bomb. But the ball spilled and was scooped up by All Blacks winger Julian Savea, and from 65 meters out he broke two tackles and touched down.
Aaron Cruden was given two chances to convert the try because he was disturbed by a laser light from the stands, but missed both chances. Still, he converted both of his penalty chances against three from Sanchez for an 11-9 halftime lead.
Prop Charlie Faumuina replaced the injured Owen Franks at halftime, but another scrum penalty was conceded and Marcelo Bosch hit it from halfway for the Pumas to lead 14-12. Cruden immediately got the lead back from his third penalty.
Flanker Sam Cane then scored out on the left wing, off Nonu's pass, after a long buildup in which New Zealand's forwards bashed the Pumas back. Moments later, from another All Blacks lineout, Nonu perfectly delayed his pass for Smith to slice through the defence and weave 40 meters to the line.
Nonu and center partner Conrad Smith played their 50th test together to tie the world record of Ireland duo Brian O'Driscoll and Gordon D'Arcy.
Pumas utility back Felipe Contepomi entered the game in the 61st to play his 86th test and equal Lisandro Arbizu and Rolando Martin as Argentina's most capped players.
The Pumas have yet to win a match in their second year but will welcome a reeling Australia to Rosario next weekend. The Wallabies only beat the Pumas by a point at home two weeks ago, and fell to South Africa 28-8 earlier Saturday.
"(Australia will be our) last game of this Rugby Championship, and we're just going to throw everything in, everything we have," said Pumas skipper Juan Martin Fernandez Lobbe.
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New Zealand 33 (Ben Smith 2, Julian Savea, Sam Cane tries; Aaron Cruden conversion, 3 penalties, Beauden Barrett conversion), Argentina 15 (Nicolas Sanchez 4 penalties, Marcelo Bosch penalty). HT 11-9.