After kick-off at the Engenhao in Rio de Janeiro had been delayed for an hour due to a floodlighting failure, Fluminense took a fourth-minute lead through striker Rafael Moura.
A corner from the left was flicked on at the near post by midfielder Edinho and Moura headed home at the far post with goalkeeper Tobias Vargas clawing the ball out in vain.
Internacional's away goal at the Centenario in Montevideo gives the Brazilian team the upper hand against Penarol, who won the last of their five South American titles in 1987.
Winger Matias Corujo put the Uruguayan side ahead eight minutes before half-time when he curled a left-footed shot inside goalkeeper Renan's right-hand post from Argentine forward Alejandro Martinuccio's cross.
Midway through the second half, Brazil striker Leandro Damiao ran onto substitute Oscar's forward pass and edged between two defenders to hit a rising shot from 20 metres that dipped over goalkeeper Sebastian Sosa and in under the bar.
"It's not such a bad result, we can play a good match there (in Brazil)," Corujo said of next week's second leg in Porto Alegre.
"They are great rivals, the last champions, but Penarol have to go out to play them as equals," he told Fox Sports.
