Messi drew a foul about 25 yards from goal in the dying seconds and stepped up to deliver what everyone came to see as his free kick sailed into the top left corner and sent the crowd into delirium.
After the goal, Messi ran toward the right corner of the field with his arms spread wide and then headed to the sidelines on the other side where he shared a hug with his family.
"I knew I had to score, it was the last play of the game and I had to score so we didn't go to penalties," Messi said on the broadcast through a translator.
"It was very important for us to get this win because it's a new tournament and it's going to give us confidence moving forward."
With four-times NBA champion LeBron James, tennis great Serena Williams and reality television star Kim Kardashian among those in the sold-out crowd, Messi entered the game as a second-half substitute to a rousing ovation with Miami ahead 1-0.
Messi was introduced as "the world's number 10" when he came into the game in the 54th minute, slipped the captain's armband on his left arm and sent the crowd into a frenzy whenever he touched the ball.
The seven-times Ballon d'Or winner did not take long to make his presence felt as he eluded some Cruz Azul defenders and led an attack down the right side, one of many chances he created on the night.
At one point, Messi ran into a Cruz Azul player in the box and fell to the ground, but while his team and supporters wanted a penalty the referee immediately wagged his finger, denying the Argentine a spot-kick.
He then set up what appeared to be the winning goal in the 89th minute but Josef Martinez, who tapped the ball into the net, was ruled offside.
But Messi, seven months removed from leading Argentina to World Cup glory in Qatar, got his chance to shine once again.
"As soon as I saw the free kick given I thought this is the way it's meant to end," said Inter Miami co-owner David Beckham. "It's so exciting tonight for our fans. All of these people that have come down here to see Leo just step on the pitch, let alone just do what he's done.
"It's a dream come true for everybody in this stadium and everybody around this country to see Leo step into the MLS and perform and I don't have many words for that."
Messi's Miami debut coincidentally came 16 years to the day after Beckham played his first game for MLS side LA Galaxy.
It has been a whirlwind week for the Argentine, whose arrival at MLS is a huge boost for the profile of soccer in the United States, who will co-host the 2026 World Cup with Mexico and Canada.
Inter Miami close out the two-game group stage on Tuesday when they host Atlanta United with hopes of advancing to the knockout stages of the Leagues Cup, which is a World Cup-style tournament featuring all teams from MLS and Mexico's Liga MX.
