The three-time champions simply had no chance against a great performance by the Argentinian side on Thursday night.
Former Liverpool forward Maxi Rodriguez opened the scoring with a right-foot volley in the 13th minute from Lucas Bernardi's cross.
Seconds before half-time, Newell's widened the gap as Nacional defender Jorge Curbelo netted an own goal.
Eight minutes after the interval, Bernardi headed a Milton Casco cross from the left and made sure of the victory, the first in Group Six for the Rosario side.
Martin Tonso made it 4-0 at the 86th minute, assisted by former Juventus and France striker David Trezeguet.
"Nacional are a very good team, but they were blocked by our very good form," Newell's midfielder Diego Mateo told Fox Sports.
In the 55th minute, after a defensive mistake, Angel Correa finished a Hector Villalba cross to net the winner.
It was San Lorenzo's first triumph after two games in Group Two and they, like Newell's, lie second.
San Lorenzo midfielder Julio Buffarini told Fox Sports: "We knew it was going to be a tough game. Independiente are more comfortable as visitors.
"In the first half we had opportunities to score. The second half was even but we managed to gain the advantage. This is an important victory."