Nino Marcelli scored with a long-range strike in the 88th for Bratislava, which ended with 10 men.
Milan moved up to 10th place in the new single-league format and within sight of the automatic qualifying spots. Bratislava has lost all five of its matches.
Milan won 3-1 at Madrid in its previous match.
Alvarez and Griezmann lead Atletico to 6-0 rout
Argentina World Cup winner Julian Alvarez scored twice and Atletico Madrid routed Sparta Prague 6-0 to move up to ninth.
Alvarez scored with a free kick 15 minutes in and Marcos Llorente added a long-range strike before the break. Alvarez finished off a counterattack early in the second half after being set up by substitute Antoine Griezmann, who then marked his 100th Champions League game by getting on the scoresheet himself.
Angel Correa added a late brace for Atletico.
Atletico beat Paris Saint-Germain in the previous round and extended its winning streak across all competitions to six matches.
Sparta remained in the elimination places with four points.
The top eight finishers in the standings advance directly to the round of 16 in March. Teams ranked ninth to 24th go into a knockout playoffs round in February, while The bottom 12 teams are eliminated.
Later, it’s: Manchester City vs. Feyenoord; Barcelona vs. Brest; Bayern Munich vs. Paris Saint-Germain; Inter Milan vs. Leipzig; Young Boys vs. Atalanta; Bayer Leverkusen vs. Salzburg; and Sporting Lisbon vs. Arsenal.
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