Winger Jherson Cordoba and striker Dorlan Pabon scored two goals apiece as Nacional, champions in 1989, ran riot against sluggish opponents at Penarol's Centenario stronghold in Montevideo.
Nacional lead Group Eight with a maximum six points having beaten Universidad de Chile 2-0 at home in Medellin last week.
Penarol, five times South American champions, have no points and have yet to score a goal after one of their worst starts in the competition. They lost 1-0 away to Argentina's Godoy Cruz last week.
"It became impossible to dominate the midfield. Our philosophy is 4-3-3 and they had greater numbers [there]," Penarol goalkeeper Fabian Carini told reporters.
Penarol captain Dario Rodriguez added: "It's tough, we weren't considering a defeat and less by such a score... losing like this makes you want to play [again] tomorrow."
There were goals inside the opening minute in two other matches. Argentina's Arsenal beat Zamora of Venezuela 3-0 in Buenos Aires in Group Four and Chile's Union Espanola came from a goal down to win 3-1 against Bolivar in La Paz in Group Three.
Jorge Ortiz gave Arsenal a flying start against the debutants, who had held six-times champions Boca Juniors to a 0-0 draw in their opening match at home last week.
The pick was Arsenal's third just before half-time with Colombian winger Carlos Carbonero, who scored their second goal, making a break down the right and steering the ball into the box where striker Luciano Leguizamon chipped over goalkeeper Alvaro Forero.
At high-altitude in the Hernando Siles stadium, Espanola made light of the rarefied air by fighting back with three goals in the final half hour after defender Edhemir Rodriguez had put Bolivar ahead in the first minute.
