Lautaro Martinez's fine goalscoring form continued as he sealed top spot for Argentina in Group A, with a 2-0 victory over Peru, who were eliminated from the competition.
With Lionel Messi out due to a groin injury, the forward stepped up, scoring at the start and end of the second half to ease any nerves after a slow first 45 minutes at the Hard Rock Stadium in Miami.
Leandro Paredes' miss from the penalty spot did not prove costly as Peru failed to threaten in what was a must-win game.
Argentina will face the runner-up of Group B in their quarter-final, while Canada take second place in the group after their 0-0 draw with Chile, while Peru make an early exit.
With a place in the quarter-finals already secured, Argentina made a slow start to the game - Alejandro Garnacho's deflected curler was their only chance in the opening 25 minutes.
The goalkeeper was required to keep things level shortly after, getting a strong hand to stop Paredes' whipped free-kick from heading into the top-left corner.
Giovani Lo Celso was then picked out on the penalty spot on the stroke of half-time, but Gallese parried his first-time shot before Garnacho fired the rebound just over the crossbar.
The half-time team talk worked wonders for Argentina, as Angel Di Maria cut Peru's defence wide open by picking out Martinez, who deftly chipped the opener over Gallese just two minutes into the second half.
Nicolas Tagliafico thought he had doubled their tally moments later, poking over the line from a corner, but it was disallowed as Lo Celso was blocking the goalkeeper's view from an offside position.
Argentina had another chance to double their lead in the 69th minute, with Jesus Castillo penalised for a handball as he slid in to block Paredes' cross in the box, and the midfielder could not profit, rattling the inside of the post with a powerful spot-kick.
In an almost carbon copy of his first goal, Martinez raced in behind once again in the 86th minute and lifted a lovely effort over Gallese, who could not get a hand to it.
Franco Zanelatto almost salvaged some pride for La Blanquirroja in the dying moments, but his thumping header bounced off the near post and, agonisingly, along the face of goal.
Martinez retains golden touch
Though Argentina were already into the quarter-finals with a game to spare, it felt like they might not be at their best without talisman Messi and manager Lionel Scaloni, who was serving a touchline ban.
However, Martinez has stepped up in this tournament, scoring in all three of their group games as he leads the race for the Golden Boot with four goals to his name.
His first two strikes both came off the bench, with his late winner sending the Albiceleste into the knockout stages against Chile, and he made the most of his first start in the tournament with an early goal in the second half.
It is just the third time this century that Argentina have won all three of their group games - the last two times (2007, 2016) they finished as runners-up, but Scaloni will be hoping they can go one better and defend their title this time around.
Peru go out with a whimper
This year's Copa America has been a tournament to forget for Peru, who go out of the tournament with just one point to their name - it is the first time they have been eliminated without a single victory since 1995.
La Blanquirroja needed a win to have a chance of snagging second spot, with hope that Canada and Chile played out a draw in the other Group A game.
However, they managed just six shots in the game, creating an expected goals of 0.14, and finish the tournament with a meagre tally of 22 efforts from their three matches without hitting the back of the net.
It was always going to be a tough ask to get a win against the defending champions, even with all of their changes, but Peru's starting front three of Bryan Reyna, Paolo Guerrero and Edison Flores not managing a single shot did not make matters easier.