Seeking a record 16th Copa America title, Uruguay dominated with 20 shots, including seven on target. Amir Murillo scored late into stoppage time for Panama.
The match drew 33,425 to Hard Rock Stadium, home of the NFL's Miami Dolphins. The stadium is the site of the July 14 final and seven games during the 2026 World Cup.
The United States defeated Bolivia 2-0 in Sunday's earlier Group C game at Arlington, Texas.
Uruguay plays Bolivia at East Rutherford, New Jersey, on Thursday, when Panama faces the U.S. in Atlanta. The group ends July 1 with a U.S.-Uruguay game at Kansas City, Missouri, and a Panama-Bolivia match in Orlando, Florida. The top two teams move on to the quarterfinals.
Uruguay is tied with Argentina for a record 15 Copa America titles but hasn't advanced past the quarterfinals since winning its last championship in 2011.
Panama failed to get past the group phase in 2016, its only previous appearance as a guest at South America's championship.
"I think we were too cautious in front of this team," Panama coach Thomas Christiansen said through an interpreter. "At some points we had a certain level of fear. The second half was a bit different. We had opportunities. We played a bit higher and did well. That's what I told the players. Even though we lost against one of the favorite contenders, we are a team that remains eager."
Araújo scored the first goal after he received a pass from Viña from just outside the penalty area, took a touch and turned. He tapped the ball twice and curled a left-footed shot past goalkeeper Orlando Mosquera's outstretched left arm for his second goal in nine international appearances.
Núñez made it 2-0 in the 85th minute after Panama turned over the ball in the center circle. Nicolás de la Cruz played a long cross to Araújo, whose header deflected off a shoulder of Murillo to Núñez. He volleyed from 12 yards for his 12th goal in 24 appearances, his ninth in his last six matches.
Viña boosted the margin to 3-0 with a header from de la Cruz's free kick in the first minute of stoppage time, outjumping defender Abdiel Ayarza for his first international goal.
Murrillo cut back the ball for space in the fourth minute of stoppage time, sending Araújo spinning, and beat goalkeeper Sergio Rochet from 15 yards in the fourth minute of stoppage time for his ninth goal.
Uruguay has undergone a rebuilding process under Argentine coach Marcelo Bielsa after the retirement of Edinson Cavani and Diego Godín, and a young roster has shown its ability to contend. Uruguay beat Lionel Messi and Argentina and also Brazil in World Cup qualifiers, then routed Mexico 4-0 in a friendly early in June.
"It's only natural that they are candidates for the title," Bielsa said through an interpreter of Argentina, a team he coached from 1999 to 2004. "As for Uruguay's expectations, we will see that and build it match by match. My expectation is that each match increasingly helps us to improve on our mistakes."
Mosquera made four saves to keep the game close until late.
Luis Suárez, the 37-year-old striker who is Uruguay's career leading scorer and was the player of the tournament in 2011, did not play.