The Bath flanker, who is 21 next month, replaces Tom Curry, who was told on his 19th birthday on Thursday that he will not be required when England go in search of a 2-0 series win.
Underhill, first spotted as a teenager by World Cup-winning flanker Richard Hill, will be assisted by Chris Robshaw, the closest thing England have had to Hill since his heyday.
England's former captain returns to the team on the blindside after an ankle injury to help boost the cap count of the starting team from the 345 of last week to 413.
It will be his first international for more than six months.
"It's great to welcome back Robbo into the squad," Jones told reporters ahead of the game at the Estadio Brigadier General Estanislao Lopez.
"He has been one of England's best players over the last two years, and he will add a lot of experience and work rate into our back row. It will also be exciting to see Sam make his debut."
Piers Francis is also set to make his first start in place of Alex Lozowski. The 26-year-old from Kent was impressive off the bench in the first test in San Juan, playing key roles in the two late tries that gave England a remarkable 38-34 win.
He has been playing for the Blues in the last two seasons, where he returns after the tour to finish the Super Rugby season, but will then take up a new deal with Northampton, thus rendering him eligible for England selection.
England captain Dylan Hartley will win his 86th cap, moving into third place on the country's list of international appearances and within five caps of Jonny Wilkinson. Jason Leonard's 114 remains a more distant target.
Hartley's understudy, Jack Singleton, the only player in the squad not to feature in last weekend's 38-34 win, could yet become the second new cap of the day.
"Argentina have lost 10 of their last 12 games, so they are going to be desperate," Jones added.
"I'm sure they're going to come out with enormous physicality. It will be another high-quality, high-pressure game and that's what we need to keep developing towards the World Cup."
Team
15-Mike Brown, 14-Marland Yarde, 13-Henry Slade, 12-Piers Francis, 11-Jonny May, 10-George Ford, 9-Danny Care, 8-Nathan Hughes, 7-Sam Underhill, 6-Chris Robshaw, 5-Joe Launchbury, 4-Charlie Ewels, 3-Harry Williams, 2-Dylan Hartley (captain), 1-Ellis Genge
Replacements: 16-Jack Singleton, 17-Matt Mullan, 18-Will Collier, 19-Nick Isiekwe, 20-Mark Wilson, 21-Jack Maunder, 22-Alex Lozowski, 23-Denny Solomona
(Editing by Ken Ferris)
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