Havili was brought into the side prior to the first week of the southern hemisphere competition to replace the injured Jordie Barrett, who needed to undergo shoulder surgery, but had not appeared in any final squads since.
His inclusion off the bench could see Damian McKenzie move from fullback to flyhalf later in the game, giving Hansen a chance to see how the 22-year-old handles the pivotal position at international level.
The All Blacks, who are on 19 points after four successive victories, can wrap up the Rugby Championship title with a win in Buenos Aires.
While Hansen tinkered with the side that beat the Springboks 57-0 two weeks ago, there was no recall for regular blindside flanker Jerome Kaino, who has not played for the team since the final test against the British and Irish Lions in early July.
The 34-year-old dual World Cup winner played all three tests against the Lions but flew home to New Zealand shortly before the Rugby Championship opener against the Wallabies in Sydney on Aug. 19.
New Zealand Rugby said at the time that an Australian media report about Kaino's private life had necessitated his return to Auckland.
Vaea Fifita has been given his second test start in the number six jersey after he showed how destructive he could be with a superb try from near halfway in the 39-22 win over the Pumas in New Plymouth earlier this month.
Hansen, however, has made something of a calculated gamble for the Pumas test as he seeks to build depth ahead of the 2019 World Cup in Japan.
He rested locks Sam Whitelock and Brodie Retallick, loose forwards Liam Squire and Sam Cane, and midfield back Ryan Crotty, with the quintet scheduled to join the side in South Africa for next week's final match against the Springboks.
Another group will return home after the Argentina leg of the trip as the All Blacks' coaching staff look to manage player workloads at the back end of a long and arduous season.
Matt Todd, who has returned from a broken hand, will replace Cane at openside flanker, while Scott Barrett and Luke Romano will lock the scrum with Patrick Tuipulotu coming off the bench.
The Pumas have never beaten the All Blacks in 25 previous test matches.
Team: 15-Damian McKenzie, 14-Waisake Naholo, 13-Anton Lienert-Brown, 12-Sonny Bill Williams, 11-Rieko Ioane, 10-Beauden Barrett, 9-Aaron Smith, 8-Kieran Read (captain), 7-Matt Todd, 6-Vaea Fifita, 5-Scott Barrett, 4-Luke Romano, 3-Nepo Laulala, 2-Dane Coles, 1-Kane Hames.
Replacements: 16-Codie Taylor, 17-Wyatt Crockett, 18-Ofa Tu'ungafasi, 19-Patrick Tuipulotu, 20-Ardie Savea, 21-TJ Perenara, 22-Ngani Laumape, 23-David Havili.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford/John O'Brien)
