The eight-time Ballon d'Or winner has bittersweet memories of the last time the Copa America was held on American soil in the 2016 centenary edition, where Argentina reached the final but lost on penalties to Chile.
Argentina held on and made the most of one of the few chances they created in the 63rd minute, when defender Nicolas Otamendi rose high to power home a Giovani Lo Celso corner.
The 36-year-old is now three Ballons d'Or clear of rival Cristiano Ronaldo, who won the last of his five trophies in 2017.
Messi was denied a hat-trick in the second half after he had a goal disallowed for offside following a VAR review.
Messi had played just 37 minutes for his club since September 3, having returned with an injury from international duty with Argentina last month.
In other qualifiers, Paraguay drew 0-0 with Peru while Colombia claimed a 1-0 home win over Venezuela.
Messi extended his winning streak since joining the MLS side to seven games.
Inter Miami crushed Philadelphia Union 4-1 to set up a title clash with Nashville SC.
Inter Miami will meet Philadelphia away on Tuesday (Wednesday 4.30 am IST) for a place in the final.
A trademark curling free-kick in the 85th minute, Messi's seventh goal in four games for Miami, took the game to a shootout after the Argentine's side had trailed 4-2 with 10 minutes to go.