Messi, 36, struck in the fourth minute of added time as his Major League Soccer side won the Leagues Cup tie.
The 20,000-capacity crowd included celebrities such as basketball’s LeBron James, tennis legend Serena Williams and US TV star Kim Kardashian.
“We wanted to start like this by giving these people a victory,” said Messi.
“We knew that it was very important for us to start this championship in winning fashion. Luckily we were able to do it in the end, and I am very happy.”
Smoke bombs in Miami’s pink colour were let off behind the goal at the DRV PNK Stadium in Fort Lauderdale. Some fans even ran onto the pitch to celebrate Messi’s goal, before being led away by security.
It continued the party atmosphere that started on Sunday when Messi was officially unveiled to fans. The unveiling was in front of another capacity crowd in South Florida.
Messi scored 32 goals in 75 games during a two-year spell with the French champions after leaving Barcelona. He turned down lucrative offers from other countries in order to play in the US.
This was the first time he had turned out for a non-European club side. He was also joined by a familiar face as he and fellow new signing and former Barca team-mate Sergio Busquets.
Busquets also came on as part of a 54th-minute triple substitution.
Spain defender Jordi Alba has also made the switch from the Nou Camp. He will be available to play against Atlanta United in the Leagues Cup on Tuesday.
The cup competition, between sides in the MLS and Mexico’s LIGA MX, marks a fresh start for Inter Miami, who are bottom of the MLS table without a win in 11 games.
Messi was on his feet with the rest of the bench to celebrate Robert Taylor’s 44th-minute opener for the home side. However, Cruz Azul’s Uriel Antuna had not read the script, canceling out Inter Miami’s lead with 25 minutes remaining.
But Argentina’s World Cup winner provided the Hollywood ending. Messi was brought down by Carlos Salcedo for a free-kick just outside the box in the final seconds. This was an ideal range for his famous left foot.
And he delivered perfectly, curling the ball high to the right of goalkeeper Andres Gudino and into the top corner.
“It is a huge joy to get this first victory after how we have done in the league,” Messi added.
“It is important to start winning, beyond the fact that it is another championship. For confidence it is very good to get victories.”
Ex-England captain David Beckham, who is co-owner of Inter Miami, watched Messi’s debut from an executive box next to the dugout.
He spotted a broad grin at the final whistle. Yesterday marked 16 years to the day since he made his own MLS debut for Los Angeles Galaxy.
“To be honest, as soon as I saw the free-kick given I thought this is the way it’s meant to end,” said the 48-year-old former midfielder.
“Especially when you’ve got players like Leo and Sergio on the pitch, that’s what they produce.
“It’s so exciting tonight for our fans. All of these people came down here to see Leo just step onto the pitch, let alone do what he’s done. It’s a dream come true for everyone in this stadium to see.
“It’s such a moment for this country, such a moment for this league.”
