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.
Di Maria has made 136 appearances for world champions Argentina since his debut in 2008, playing in four World Cups and scoring in the 2022 final win over France.
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.
It was a cathartic evening for Luis Diaz who, just a few days after Colombia guerrillas freed his kidnapped father, scored twice within four minutes late in the second-half to give his country the upset win over Brazil.
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.
Argentina moved top of the CONMEBOL standings after beating Paraguay 1-0 to maintain their 100 per cent record.
Angel Di Maria took over as captain in Messi's absence and shone, providing two assists before halftime
In other qualifiers, Paraguay drew 0-0 with Peru while Colombia claimed a 1-0 home win over Venezuela.
Inter Miami crushed Philadelphia Union 4-1 to set up a title clash with Nashville SC.