Harry Kane scored two goals for Bayern Munich, with Trevoh Chalobah also contributing an own goal for the German side.
Cole Palmer scored Chelsea's sole goal, striking back quickly after Bayern had taken a two-goal lead.
Chelsea, playing in the Champions League for the first time in nearly two and a half years, displayed ambitious football but were ultimately overcome by Bayern's greater experience and quality.
The match saw Bayern score two quick goals, followed by Chelsea's immediate response, before Kane secured Bayern's two-goal advantage in the second half.