The All Blacks were facing the prospect of three straight defeats for the first time in 22 years after losses to Argentina and the Wallabies.
But they comfortably prevented that, leading 10-0 at halftime before pulling away with four second half tries, including two to Will Jordan which gave the All Blacks a bonus point win.
The All Blacks' five tries means they will secure the title if Argentina or Australia do not win the final match of the tournament in Sydney next weekend by a substantial margin.
The victory ended New Zealand's first losing streak of more than one match since 2011 and Argentina's fairytale run in the tournament after their first win over the All Blacks was followed by a draw with Australia last week.
The Pumas had not played any test rugby for more than a year before they arrived in Australia but will still be disappointed to be held scoreless in a test match against the All Blacks for the first time.
Hooker Dane Coles scored the first try in the corner in the 12th minute and Richie Mo'unga added a penalty soon afterwards to give the All Blacks a 10-0 halftime lead, but New Zealand really opened up after the break.
Ardie Savea bulldozed over the line from an attacking lineout and replacement back Will Jordan scored two tries in three minutes off an Argentine error and an intercept before lock Patrick Tuipulotu blew out the score after the hooter.
The Pumas wore black armbands in memory of soccer great Diego Maradona and New Zealand captain Sam Cane laid the gift of an All Blacks shirt emblazoned with the name of the Argentine star on the turf before the haka.
There was no sentiment from the New Zealanders after kickoff, however, as they went back to basics with setpiece dominance, hard running and judicious kicking to put sustained pressure on the Pumas.
Argentina made 10 changes to the side that drew with Australia last week which may account for a lack of fluency in some of the combinations and a string of handling errors. (Reporting by Nick Mulvenney, editing by Hugh Lawson)