The Ivorian netted early after Marko Gobeljic handled a Rade Krunic strike, before El Fardou Ben drew the Serbian champions level on the night with a well-taken goal. The Rossoneri were aided by a red card shown to Gobeljic in the second half, curtailing the visitors’ attacking intent.
After a 2-2 draw in Belgrade in the first leg, Milan saw off a spirited Red Star effort to seal victory on away goals, although they have now failed to win in four matches in all competitions.
Milan made a flying start and were awarded a penalty with little more than five minutes gone when Krunic’s shot cannoned off Gobeljic’s hand in the box.
Kessie stepped up and made no mistake from the spot, before displaying a touching tribute to compatriot Willy Braciano Ta Bi, after the Atalanta youngster tragically passed away this week.
At the other end, a quick one-two allowed Ben to work space in the area but his shot lacked control and sailed wide of the far post, as Red Star reacted well to going behind.
The visitors found the back of the net after Ben scrambled in from a corner, but the goal was chalked off after the ball came off the arm of Radovan Pankov. Ben was causing panic in the Milan defence and clipped the crossbar with a freekick from the edge of the box.
The Serbians’ pressure finally told on 25 minutes as Ben netted the goal his early play deserved. The Comoros international latched onto a clever Mirko Ivanovic through-ball to rifle across Gianluigi Donnarumma and in off the foot of the post.
Milan began to regain their grip on the match and wasted a chance to retake the lead before half-time, as Hakan Calhanoglu found Diogo Dalot at the back post but the full-back could only fire at Milan Borjan.
The Rossoneri came out on the front foot in the second half, with Zlatan Ibrahimovic bending an effort wide before setting up fellow substitute Ante Rebic for a close-range header, although his attempt was off target.
Red Star continued to push forward and take the lead, with Ivanic coming close as he dribbled into the box and saw a deflected shot whistle inches past the post.
Milan had Donnarumma to thank for remaining ahead with 20 minutes to go, as he produced a stunning point-blank save from Sekou Sanogo after the Ivorian looked to net from a flick on at a freekick.
The visitors’ task was made all the more difficult as Gobeljic was shown a second yellow card for a clumsy challenge on Calhanoglu, and Milan almost took advantage immediately as Ibrahimovic set up Alexis Saelemaekers, though the Swede was flagged offside in the build-up.
With Aleksandar Katai blasting into the side-netting with the goal at his mercy late on, Milan held out for a draw and victory in the tie, booking their place in the next round.