Cruzeiro and Argentine side Velez Sarsfield lead the group on seven points, Chile's Colo Colo have four and Deportivo Italia one. Velez host Colo Colo on Thursday in Buenos Aires.
The Brazilians took the lead following a sixth-minute corner when Italia goalkeeper Jose Fernandez was caught stranded and Fabinho stooped to head the ball through a melee of players.
Italia midfielder Alain Giroletti rattled the bar with a free-kick close to the half-hour mark before Pedro Ken increased Cruzeiro's lead in the 69th minute, two minutes after coming on as a substitute.
In Group Four, Argentina's Lanus beat Blooming of Bolivia 1-0 thanks to a penalty from Santiago Salcedo to climb within two points of joint leaders Libertad of Paraguay and Peruvian champions Universitario.
STALEMATE IN CHILE
In Group Seven, Universidad Catolica of Chile needed a late equaliser from forward Juan Jose Morales to scrape a 1-1 draw at home to Caracas FC.
The Venezuelan side took the lead five minutes after halftime through defender Jaime Bustamante, who volleyed home from Dario Figueroa's free-kick.
Striker Zamir Valoyes could have given Caracas victory but his two efforts in quick succession hit the woodwork four minutes from time. In their next attack Pablo Camacho hit the post.
Catolica fans jeered the team after their poor performance and called for coach Marco Antonio Figueroa to be sacked.
The result leaves both teams in danger of elimination.
