The former logistics manager of the Sinaloa cartel testified at trial Thursday against his former boss Joaquín “El Chapo” Guzmán, giving jurors a rare opportunity to hear details of alleged high-level discussions within the cartel’s inner circle.

The testimony of Vicente Zambada Niebla, who was arrested in Mexico in 2009 and extradited to Chicago, was highly anticipated. Mr. Zambada served among the leadership of the Sinaloa cartel for nearly a decade and recently pleaded guilty to drug-conspiracy charges. Officials have called...