Goals from Jorge Rodriguez and Jonathan Rodriguez gave Penarol - Uruguay's most successful club - the win over their Bolivian opponents at the Estadio Centenario on Wednesday.
Midfielder Jorge Rodriguez opened the scoring after 12 minutes in Montevideo - his second goal in less than a week.
Penarol team-mate Jonathan Rodriguez doubled the home side's lead five minutes from time and provided Jorge Fossati's men with a healthy lead heading into next week's return leg in Cochabamba.
General Diaz and Nacional Potosi were the other host teams to win their first-round matches on Wednesday.
Humberto Garcia's General Diaz accounted for Chile's Cobresal 2-1 at the Estadio Feliciano Caceres in Paraguay.
Scores were level at half-time after Cobresal's Patricio Jerez cancelled out Gustavo Toranzo's 14th-minute opener.
General Diaz managed to walk away with a slender advantage thanks to Roberto Gamarra, who found the back of the net in the 71st minute.
At the Estadio Victor Agustin Ugarte, Charles Da Silva's 11th-minute goal helped Bolivian side Nacional Potosi to a 1-0 victory over Paraguay's Libertad.
In other results, Atletico Nacional will return home to Colombia full of confidence following their 1-1 draw at Venezuela's Deportivo La Guaira.
Framber Villegas' 66th-minute opener appeared to have set Deportivo La Guaira on their way to a narrow win, only for Edwin Cardona to equalise from the penalty spot with seven minutes remaining.
Meanwhile, UTC Cajamarca and Deportivo Cali of Colombia played out a scoreless draw in Peru.
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
