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 Estéban Andrada produced an incredible save to deny Alejandro Meleàn at Estadio Felix Capriles.
Elsewhere in Group G, Athletico Paranaense lost 1-0 against Deportes Tolima.
Brazilian side Flamengo defeated San Jose 1-0 away from home in a Group D victory.
Adriàn 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.