Paris Saint-Germain midfielder Di Maria, who was promoted to the starting line-up for the final, coolly lobbed over Brazil goalkeeper Ederson for the 22nd-minute winner.
#CopaAmérica 🏆— Copa América (@CopaAmerica) July 11, 2021
¡TREMENDA DEFINICIÓN! Ángel Di María recibió el pase de Rodrigo De Paul y la tiró por arriba de Ederson para el 1-0 de @Argentina
🇦🇷 Argentina 🆚 Brasil 🇧🇷#VibraElContinente #VibraOContinente pic.twitter.com/OuFUmqipVA
Argentina had been Copa runner-up at four of the past seven tournaments, losing to rival Brazil in 2004 and 2007, but finally claimed the country's 15th continental crown.
The triumph also marks Lionel Messi's maiden piece of major silverware with Argentina, with the six-time Ballon d'Or winner dominant throughout the tournament, finishing with most goals (four) and most assists (five).
In a physical encounter, Brazil superstar Neymar received plenty of attention while Messi was unable to exude his normal influence for La Albiceleste.
Brazil started the better but could only manage scuffed efforts on goal from Everton and Richarlison before Argentina struck against the run of play.
The outstanding Rodrigo De Paul's hopeful ball forward eluded Selecao left-back Renan Lodi, allowing Di Maria in behind and he calmly poked over the onrushing Ederson.
Di Maria was a constant threat in the first half, with a left-foot effort blocked by Marquinhos before Messi flashed wide.
With the half-time injection of Roberto Firmino, Brazil pressed and thought it had equalised in the 52nd minute when Richarlison hit the back of the net but was offside in the lead-up.
The Everton forward tested Argentina keeper Emiliano Martinez at his near post shortly after, with the Aston Villa man saving smartly.
Brazil substitute Gabriel Barbosa had a late volley brilliantly thwarted by Martinez, before an exhausted Messi spurned a golden opportunity to seal the win from De Paul's throughball.