Di Maria, starting for just the second time in the Copa, justified his selection by scoring the opener midway through the first half.
Renan Lodi failed to cut out a long ball forward from Rodrigo De Paul and Di Maria lobbed the stranded Ederson with aplomb.
Brazil piled on the pressure in an exciting second half but even with five strikers on the field they could not get an equalizer against an Argentine defense protected by the outstanding Rodrigo De Paul.
“First we have to congratulate our opponents especially for the first half when they neutralized us,” said Brazilian defender Thiago Silva.
“In the second half there was no contest – only one team tried to play football, the other just wasted time as we knew they would. It’s not an excuse, we didn’t do what we had to, principally in the first half.”
Argentina’s win was a particular triumph for Barcelona striker Messi, who picked up his first ever title in a blue-and-white shirt after more than a decade of club and individual honors.
The Argentine players surrounded their captain at the final whistle. Goalkeeper Emilian Martinez celebrated what he called a Maracanazo, a remarkable win at the famous Rio stadium.
“I’m speechless,” he said. “I knew my dream would come true, and where better than the Maracanazo and giving the title to the best in the world and fulfilling his dream.”
Messi finished the tournament’s joint top goalscorer with four goals and was elected joint best player along with Neymar.
But he was quiet throughout the game at the Maracana stadium and uncharacteristically missed a golden opportunity to wrap the game up with two minutes remaining.
When the final whistle went, Argentina TV declared “Argentina Champions, Lionel Messi Champion!”
The match itself was a disappointing one, with Argentina the better side in a cagey first half that featured 21 fouls.
However, Brazil came out more aggressively in the second period and as the time ticked on they threw more people forward – and at one point having five recognised strikers on the field.
Richarlison had a goal chalked off for offside seven minutes into the second half and then forced Emiliano Martinez into a good stop two minutes later.
But as Brazil poured forward gaps, opened up and Argentina missed two clear chances to score in the dying moments of the match.
The victory was Argentina’s 15th Copa America triumph and means they draw level with Uruguay as the all-time leading winners.
“This is a very big title,” said Argentine coach Lionel Scaloni. “I hope that Argentines can enjoy it. The fans love the team unconditionally and I think they identify with this side that never drops its guard.”
Their win extended their sequence of undefeated matches to 20 under Scaloni and handed Brazil their first competitive defeat since they lost to Belgium in the quarter-finals of the 2018 World Cup.