Lautaro Martinez scored twice at the Hard Rock Stadium to seal a win that ensured Argentina advance to the quarter-finals as Group A winners.
With Messi sidelined after complaining of a sore right hamstring, and coach Lionel Scaloni serving a one-game suspension, Argentina made nine changes to their starting XI at the Hard Rock Stadium.
But despite the makeshift-looking line-up, Argentina were always in control against a disappointing Peru side who managed just one shot on goal during a one-sided encounter.
Martinez's first goal came just after half-time. A sublime through ball from Angel Di Maria released the Inter Milan forward, who calmly lifted a deft finish over advancing Peru goalkeeper Pedro Gallese.
Argentina had a chance to double their lead in the 72nd minute after Jesus Castillo handled in the area to concede a penalty.
But Leandro Paredes crashed his ensuing spot-kick against the woodwork to leave the score at 1-0.
Martinez then grabbed a second in the 86th minute, latching on to a long pass forward before finishing past Gallese.
Replays indicated Martinez appeared to shove defender Aldo Corzo in the build-up but referee Cesar Ramos waved Peru's protest and the goal stood.
"It was tough in the first half because they were defending deep, but the first goal opened up the game," Martinez said afterwards. "There's a lot more to come from us."
Martinez has now scored in four consecutive appearances for Argentina and is relishing his hot streak.
"Every time I put on this shirt, every training session, every meal, every team talk, I enjoy it," Martinez said.
Argentina will now face the runner-up from Group B in the quarter-finals in Houston next Thursday, most likely either Ecuador or Mexico.
In Saturday's other Group A game, Canada held 2015 and 2016 Copa America champions Chile to a 0-0 draw in Orlando, which was enough to see the Canadians into the last eight.
Chile needed a victory to leapfrog the Canadians into the knockout rounds but were left with a mountain to climb early in the game when Gabriel Suazo was dismissed for a second yellow card after only 27 minutes.
"It took a lot of hard work -- it's our first time in this competition and it's not easy," Canada captain Alphonso Davies said about his team's advance to the last eight.
"There's a lot of good teams in this competition and a lot of good players. But we stuck to our plan and we played well. We showed a lot of fight. We had to show our teeth at times, but overall we did well."
Canada will play the winners of Group B in the quarter-finals.
