Darwin Nunez scored as Uruguay ended Argentina's 14-match winning run going back to the 2022 World Cup.
The Liverpool forward slotted home in the 87th minute after Ronald Araujo had opened the scoring in the 2026 World Cup qualifier in Buenos Aires.
World Cup winners Argentina had not lost since their 2-1 defeat by Saudi Arabia in their first match at the Qatar tournament last year.
"We never felt comfortable," said Argentina captain Lionel Messi.
"The loss is a good test for us. They are an intense team and it was difficult for us to play our game.
"They have physical and fast players in the midfield. We didn't find a way to possess the ball for a long period of time."
It was the first time Messi had failed to score for his country, when playing, since their World Cup group-stage win over Poland.
Araujo's opener for Uruguay was the first goal Argentina have conceded since the World Cup final against France - a run of eight matches.
Uruguay appointed former Leeds boss Marcelo Bielsa as head coach in May and Messi said the Argentine's influence is already clear.
"You can see Bielsa's hand on the way Uruguay is playing," Messi said. "In all the national teams or clubs, including Argentina, his style was very recognisable. And he has a good generation of players."
Argentina, who had won all four of their opening qualifiers, remain top of the standings with 12 points from five matches while Uruguay are second with 10 points.