Micah Hamilton became the youngest English player (20 years, 30 days) to score on his Champions League debut since Marcus Rashford in 2017 for Manchester United (19 years, 316 days)
Hamilton, 20, has been with the club since the age of nine and put City ahead after 19 minutes in a hostile atmosphere in Serbia.
Matheus Nunes found him down the right wing and Hamilton, who has represented England at under-16 level, got into the penalty area and shifted the ball to create space before powerfully firing into the roof of the net.
On a great night for City's academy, 20-year-old Oscar Bobb also scored his first goal for the club with a jinking run at the home defence, before curling in the second on 63 minutes.
Hwang In-beom pulled one back for Red Star when he got free of marker Kalvin Phillips and shot low past Stefan Ortega.
But Phillips made amends when he converted a penalty, after the impressive Hamilton had been fouled.
Aleksandar Katai headed in a late second for Red Star, but European champions City were not to be denied and follow in the footsteps of Real Madrid to advance into the last 16 with six wins from six group matches.
Pep Guardiola's side become only the second English team to achieve this, after Jurgen Klopp's Liverpool in 2021-22.
The draw for the last 16 will be held at Uefa's headquarters in Nyon, Switzerland at 11:00 GMT on Monday, 18 December.
City will face one of the sides to have progressed as group runners-up, with one of their potential opponents being Inter Milan - the team they beat in last season's final.
-- Courtesy of BBC Sport