Cavani and Luis Suarez scored as Uruguay opened their Group C campaign with a 4-0 demolition of 10-man Ecuador in Belo Horizonte.
Ecuador's Jose Quintero was sent off after Nicolas Lodeiro gave Uruguay a sixth-minute lead and it was one-way traffic from that point.
Cavani, Suarez and an own goal sealed a routine outing for Oscar Tabarez's Uruguay and the former revelled in the result.
"We are ready to fight in the Copa America," Cavani said post-game, with 15-time champions Uruguay seeking their first Copa title since 2011.
"We had chances in the first half, we could do it and that gave us the calm to handle the game. It was an important step."
Cavani, who scored his first Copa goal after 11 matches, added: "We knew they were going to be a very difficult opponent. The important thing was that we entered the game with maximum concentration and we achieved that."
After Paris Saint-Germain forward Cavani made it 2-0 past the half-hour mark, Suarez tripled the lead prior to the interval following Quintero's 24th-minute dismissal.
Suarez – who missed the end of Barcelona's season due to knee surgery – converted at the back post to heap further misery on Ecuador.
Mina then turned the ball into his own net with 12 minutes remaining – a goal that had been initially ruled out for offside before being overturned by VAR.
"Obviously, it's a positive result because we play the way we wanted to," Suarez told reporters. "But we played with an extra man in the first half.
"We will play the tournament with the same hope and the same desire prior to today's result."