The 36-year-old Argentine legend scored twice in the first 22 minutes before assisting Robert Taylor in the second half.
Messi celebrated his second goal by gesturing at Inter-Miami owner David Beckham.
His performance this week followed a match-winning free kick in stoppage time on his debut last week.
“He’s able to do everything with the ball. Taylor remarked, “He can maintain his composure in confined areas, and he always makes the right choice.”
“He will typically locate one of his teammates. He contributes so much quality to the team. I mean, he is the world’s greatest player.
“He scores two goals, as he did in the previous game, and receives another assist. It’s an absolute pleasure to engage with him.”
Messi, a seven-time winner of the Ballon d’Or, began training with his new Major League Soccer team for the first time last week, following the expiration of his contract with Paris Saint-Germain.
The World Cup champion of 2022 scored 32 goals in 75 games during a two-year stint with the French champions but declined lucrative offers from other countries to play in the United States.
Messi opened the scoring in the ninth minute, converting a ricochet from his own shot after controlling an over-the-top pass from Sergio Busquets, a former Barcelona teammate and new arrival.
He doubled the advantage 13 minutes later, combining with Finland midfielder Taylor to convert a close-range cross.
Taylor added a third goal before halftime, and Messi assisted the 28-year-old to conclude the scoring in the second half.
Messi was replaced in the 78th minute to a standing ovation, and shortly thereafter, a number of supporters left the 20,000-seat DRV PNK Stadium.
“I truly did not observe. However, given the type of player he is, it is understandable that this occurs,” Inter Miami head coach Gerardo Martino said.
“I would have preferred that the crowd stayed to honor the entire team, but I also understand why they left.”
With the victory, Inter Miami advanced to the knockout round of the League Cup.