The defending champions had already secured their place in the last 16 as Group G winners, allowing Pep Guardiola the luxury to make nine changes.
Bobb and Hamilton were two of the youngsters given their chance to shine on European football's biggest stage and reveled in the occasion.
A picture of Hamilton receiving instructions from Guardiola as a ball boy in 2017 went viral ahead of kick-off.
And he rewarded his manager's faith to start the game by firing high past Omri Glazer from a narrow angle on 19 minutes.
Bobb has featured more prominently in first-team squads this season and the Norwegian's solo run and cool finish doubled City's lead early in the second half.
Red Star also had only pride to play for as they were guaranteed to finish bottom of the section before kick-off.
Hwang In-beom pulled a goal back for the Serbian champions.
But Hamilton impressed once more as he won a penalty and Kalvin Phillips stepped up to score his first City goal five minutes from time.
Aleksandar Katai struck for Red Star in stoppage time, but City held on to become just the second English side to win all six Champions League group games after Liverpool in 2021/22.