Cruzeiro, who lost the 2009 final to the Argentine team, got their first win in La Plata at the fourth attempt having crushed Estudiantes 5-0 at home in their Group Seven opener in February.
Thiago Ribeiro put the Brazilian side ahead in the 11th minute when he slotted fellow striker Wallyson's cross home at the far post.
Man-of-the-match Wallyson took his personal tally to six when he gave his side a 2-0 half-time lead with a fine solo goal in added-time, sneaking between two defenders to round goalkeeper Agustin Orion and shoot into the roof of the net.
Left-back Gilberto made it three in a lightning counter-attack eight minutes from the end of a rain-soaked second half at the Ciudad de La Plata stadium.
"The Libertadores is tough so we always mark hard when we don't have the ball, then when we are in possession we try to play attractive football in the Brazilian style," right back Pablo told Fox Sports of Cruzeiro's mix between strong defence and fast counter-attacks.
Cruzeiro finished the group phase with 16 points from five wins and a 0-0 draw - away to Deportes Tolima of Colombia - and a goals tally of 20-1.
Four times South American champions Estudiantes, who had also already qualified before Wednesday's matches, finished second with 10 points and Tolima third with eight.
Paraguay's Guarani lost their last match 2-0 at home to Tolima to notch up six defeats and a goals count of 2-16.
Teams to have qualified so far for the last 16 also include former champions LDU Quito, Penarol and Gremio, Colombia's Atletico Junior and Libertad of Paraguay.
