The All Blacks, who have already clinched the title with five straight victories, came under pressure from the Pumas late on, conceding two tries and having two men sin-binned.
Centres Anton Lienert-Brown and Ryan Crotty, hooker Dane Coles, scrumhalf TJ Perenara and fullback Ben Smith went over for New Zealand between the 28th and 45th minutes with Beauden Barrett converting four tries.
Pumas number eight Facundo Isa and fullback Joaquin Tuculet scored tries in the last 22 minutes as Argentina hit back, with New Zealand's Joe Moody and Liam Squire earning yellow cards.
New Zealand are now one win shy of matching the record for top-tier nations held by the All Blacks (1965-69, 2013-14) and South Africa (1997-98).
Argentina had given a good account of themselves despite losing 57-22 when the teams met three weeks ago in Hamilton and had planned to pace themselves better on Saturday to ensure they were not overrun late on.
However, that plan went awry when they conceded four tries in the last 12 minutes of the first half, two of them right before halftime.
A Barrett penalty was all that separated the sides until the 28th minute when Lienert-Brown found a gap from a scrum to dart through for his first test try.
Crotty scored seven minutes later after a poor lineout throw by Argentina and the hosts were then stunned by two more tries in the final minute of the first half.
A kick ahead by centre Santiago Gonzalez Iglesias was charged down and Coles touched down, then from the restart and with the hooter about to sound, Perenara ended another break to go over for a 29-3 halftime lead.
New Zealand carried the momentum into the second half and Smith went over from Lienert-Brown’s inside pass.
Argentina regained the initiative after a fine break by wing Santiago Cordero and Tuculet almost ended with a try.
Prop Moody was sin-binned for a foul and Argentina opted for a five-yard scrum. After several attempts to break down the All Blacks defence, the impressive Isa found a gap under the posts in the 58th minute.
Three minutes after Moody’s return, New Zealand found themselves a man short again after flanker Squire was yellow carded.
The home side were rewarded for their late pressure when Tuculet scored in the corner and Gonzalez Iglesias kicked a fine conversion from the touchline.
New Zealand top the table with 25 points followed by South Africa on 10 after their 18-10 win in Pretoria against Australia. The Wallabies have nine points while Argentina are bottom of the standings with five.
In the last round of matches next Saturday, New Zealand visit South Africa and Argentina play Australia at Twickenham in London in the first Championship test to be played outside the southern hemisphere.
(Reporting by Rex Gowar; Editing by Peter Rutherford)
