Before assisting teammate Robert Taylor in the second half, the 36-year-old Argentina star scored twice in the first 22 minutes.
Messi pointed at David Beckham, the owner of Inter Miami, after scoring his second goal.
His performance comes after a game-winning stoppage-time free kick on his debut last week.
“He can do everything on the ball. He can keep it in tight spaces, and he makes the right decision 100% of the time,” Taylor said in a post-match interview. “Most of the time he’ll find one of his team-mates.
“He brings so much quality to the team, so much. I mean, he’s the best player in the world.
“This is what he does – he scores two goals, he scored last game, gets another assist. It’s a dream come true to play with him.”
Messi, a seven-time Ballon d’Or winner, joined the Major League Soccer team after his contract with Paris St. Germain expired and only began training with his teammates last week.
During a two-year stint with the French champions, the 2022 World Cup winner scored 32 goals in 75 games and declined lucrative offers from other nations to play in the US.
In the ninth minute, Messi scored the game’s first goal by converting a rebound of his own shot after controlling a pass over the top from fellow newcomer and former Barcelona teammate Sergio Busquets.
Thirteen minutes later, he doubled the advantage by teaming up with Finland midfielder Taylor to bury a low cross from close range.
Before the half, Taylor added a third, and Messi finished the scoring by putting the 28-year-old through on a break in the second period.
Messi was substituted in the 78th minute to a standing ovation, with a number of fans leaving the 20,000-seat DRV PNK Stadium shortly afterwards.
The win saw Inter Miami move into the knockout stages of the Leagues Cup.
The Leagues Cup is a tournament which brings together all the top-flight teams from MLS and Mexico’s Liga MX and with two wins Miami top their group and with their new arrival looking settled so quickly, they will surely believe they can get their first-ever trophy.
