Reeling from Red Star's last-gasp equaliser in the first leg and Monday's (AEDT) 3-0 derby defeat to Serie A title rivals Inter, Milan just did enough to secure its progress on Friday – and they had birthday boy Gianluigi Donnarumma to thank.
Franck Kessie's early penalty put Milan 3-2 up on aggregate, but Red Star hit back through El Fardou Ben.
With Milan profligate at the other end, 22-year-old Donnarumma had to pull off an outstanding stop to deny Sekou Sanogo, before Marko Gobeljic's red card dented Red Star's comeback hopes.
A penalty was the reward for Milan's bright start when VAR adjudged Gobeljic to have purposefully handled Rade Krunic's shot.
Kessie made no mistake from the resulting spot-kick, his thumping strike sending Milan Borjan the wrong way.
Yet Red Star fought back, and after Ben saw a goal disallowed and hit the crossbar with a wicked free-kick, the Red Star winger drilled a crisp finish beyond Donnarumma.
Diogo Dalot should have restored Milan's lead, yet struck straight at Borjan, and he was almost punished when Guelor Kanga's thunderous hit whistled wide.
Stefano Pioli wasted no further time in attempting to wrest back control, introducing Zlatan Ibrahimovic and Ante Rebic at the interval.
The duo almost combined eight minutes after the restart – Rebic just failing to divert Ibrahimovic's header home.
Donnarumma came up with a reminder of his talent after the hour, somehow keeping out Sanogo's close-range volley, with Gobeljic slicing wide on the rebound.
Gobeljic compounded Red Star's frustration moments later when he charged in on Hakan Calhanoglu to pick up a second booking, and though Alexis Saelemaekers had a goal disallowed for offside, Milan nevertheless made their numerical advantage count to advance.