Last season's runners-up Boca Juniors were held by Bolivian hosts Jorge Wilstermann in Group G on Tuesday.
Boca Juniors' Copa Libertadores campaign started with a goalless draw at Jorge Wilstermann, while Flamengo edged San Jose.
Boca finished runners-up to bitter rivals River Plate in last season's controversial final, which had to be moved to Real Madrid's Santiago Bernabeu due to fan issues and the club's bus being attacked.
Back in action in South America's premier club competition, Boca were held by Bolivian hosts Jorge Wilstermann in Group G on Tuesday.
Jorge Wilstermann almost stunned Boca in the 68th minute but goalkeeper Esteban Andrada produced an incredible save to deny Alejandro Melean at Estadio Felix Capriles.
Elsewhere in Group G, Athletico Paranaense lost 1-0 against Deportes Tolima.
Brazilian side Flamengo – who reached the last 16 in 2018 – defeated San Jose 1-0 away from home.
Gabriel 'Gabigol' Barbosa – on loan from Serie A side Inter this season – was the difference in Bolivia, where his 60th-minute goal saw Flamengo to a Group D victory.
Adrian Martinez scored twice in the opening four minutes as Libertad routed Universidad Catolica 4-1 in Group H, Melgar and San Lorenzo played out a 0-0 draw in Group F, while Godoy Cruz and Olimpia drew by the same scoreline in Group C.