Out by 31-10 at halftime, the All Blacks struggled as Argentina battled back to 24-31 as loose forwards Pablo Matera and Marcos Kremer, and hooker Julian Montoya, pushed the All Blacks hard while first five-eighths Tomas Albornoz controlled their performance and scored a superb try.
But, once they cleared their mistakes, the All Blacks looked the dominant side, especially in lineouts where loose forward Tupou Vaa'i, lock Fabian Holland and replacement Patrick Tuipulotu took charge.
In the loose, Ardie Savea was in his element, and Vaa'i continued his growth on the blindside flank.
After an exchange of penalty goals to All Blacks first five-eighths Beauden Barrett and his opposite Albornoz, the All Blacks put their lineout maul to use for hooker Codie Taylor, Holland, and prop Fraser Newell to each charge at the line before the ball was released to the backs.
Fullback Will Jordan passed over the head of his marker for wing Sevu Reece to reel the ball in before it went over the sideline and scored in the eighth minute.
Argentina got their first chance in the All Blacks' 22m area and made the most of it with several attempts to break through the middle of the rucks. But it wasn't until they fed their backs that a pass from second five-eighths Santiago Chocobares was lobbed to wing Rodrigo Isgro, who scored out wide.
However, in play after the restart, a cynical foul by prop Mayco Vivas resulted in him receiving a yellow card. It took the All Blacks six minutes, but they finally took advantage after Savea, who was again in his burgling best in mauls, drove through tackles to get momentum.
The ball was moved wide through the backs, where Jordan side-stepped inside a defender to run into space and feed the supporting halfback Cortez Ratima, who scored in the 23rd minute.
Argentina's desperation resulted in them conceding penalties that allowed the All Blacks to kick deep to the corners for lineouts, twice in the last five minutes.
First, at their second attempt, it was Savea on the back of a lineout maul who scored in the 37th minute, and then after second five-eighths Jordie Barrett was used to gain extra distance from inside the All Blacks' half. Another lineout drive allowed Ratima to probe deep into the goalmouth, and after centre Billy Proctor and flanker Du'Plessis Kirifi carried on, it was moved wide for Reece to score his second try, two minutes into extra time.
The first 10 minutes of the second half were untidy from both sides before the All Blacks made their first substitutions before a scrum 15m from their line. But Argentina struck when replacement halfback Finlay Christie and Jordie Barrett were unable to contain Albornoz, who took advantage, running against the grain, to score under the crossbar.
As Argentina lifted the tempo of their game, and utilised more possession, the All Blacks started to concede penalties in their 22m, and the home benefited, with centre Billy Proctor infringed as Matera ran hard to the line, and was sin-binned. Argentina's confidence lifted as it opted to take a scrum from a penalty, and then next used a tap penalty.
From that play, it was No8 Joaquin Alviedo who put the ball down beside a goalpost to get Argentina to 24-31 down.
That proved the spark to ignite the All Blacks' response, and it was the choice to kick to the corners from penalties that, at the second attempt, saw replacement hooker Samison Taukei'aho use his strength off the maul to score and put more distance between the sides.
A carbon copy in the 73rd minute saw Taukei'aho over again to frustrate the home's ambitions.
There was still time for the All Blacks to concede another yellow card when replacement centre Anton Lienert-Brown was involved in a head-on-head clash with Chocobares three minutes from the end.
Consistency and fluidity across the game were still elusive for the All Blacks, but they showed that when they were able to gain control, they had too much skill for the Argentinians to contain.
Scorers: Argentina 24 (Rodrigo Isgro, Tomas Albornoz, Joaquin Alviedo tries ; Albornoz 3 con, pen). New Zealand 41 (Sevu Reece 2, Cortez Ratima, Ardie Savea, Samisoni Taukei'aho 2 tries; Beauden Barrett 4 con, pen). HT: 10-31