Palmeiras forward Keirrison turned in Cleiton Xavier's pass from close range to open the scoring after three minutes in Sao Paulo and added the second for the Brazilians with a 20th minute penalty after a foul on Willians.
Edemir Rodriguez pulled one back for the Bolivians two minutes later after a blunder by Palmeiras goalkeeper Marcos but Diego Souza restored Palmeiras' two-goal lead five minutes before halftime.
Cleiton Xavier scored the fourth with a long-range swerving shot in the 58th minute and former Brazil midfielder Edmilson headed a fifth in the 90th.
Palmeiras coach Luxemburgo has won the Brazilian championship a record five times with four different clubs but the Libertadores has always eluded the former Real Madrid and Brazil boss.
Palmeiras' only worry is that the second leg will be played at nearly 4,000 metres above sea level in the mining town of Potosi.
In Lima, Peruvians Sporting Cristal came from behind to beat Argentina's Estudiantes 2-1 in a game of goalkeeping mis-haps.
Enzo Perez put the visitors ahead from a narrow angle after his shot found a gap between Manuel Heredia and the post after 28 minutes.
Cristal equalised in the 40th minute when Roberto Palacios' header somehow looped over Estudiantes goalkeeper Mariano Andujar and Hector Hurtado slotted home the winner nine minutes after halftime.
