Bologna s Polish goalkeeper Lukasz Skorupski deflects a shot during the Italian Serie A football match between AC Milan and Bologna on April 4, 2022 at the San Siro stadium in Milan. AFP
The result left Milan just one point ahead of second-place Napoli with seven matches remaining. Defending champion Inter Milan was four points behind its city rival but having played a match fewer.
It was Bologna's first match since coach Sinisa Mihajlovic returned to hospital for treatment for leukaemia. He beat the disease in 2019.
Mihajlovic briefly coached Milan six years ago and there was message of support for him on the big screens before the match.
Bologna hasn't scored a goal since February, the same round in which Milan last conceded a goal, but it was the visitors who had the better of the early chances with Rossoneri goalkeeper Mike Maignan forced into a number of saves including a fantastic one to fingertip a scorching shot from Musa Barrow over the bar.
Milan had chances of its own and Theo Hernandez sent a powerful effort just past the right post in the 33rd minute.
It went even closer on the stroke of halftime with a towering header from Olivier Giroud, which was stopped by Bologna goalkeeper Lukasz Skorupski.
Milan should have broken the deadlock in the 61st but Davide Calabria's shot was deflected just past the far post by a last-ditch sliding tackle from Bologna defender Gary Medel.
Zlatan Ibrahimovic, who is returning from injury, was brought on with 20 minutes remaining but the veteran Milan forward was unable to change the result.
Ibrahimovic was left bleeding and finished the match heavily bandaged after a clash of heads with Medel, who was unable to continue.
Relegation-threatened Genoa suffered its first defeat under coach Alexander Blessin as it lost 1-0 at Hellas Verona.
Genoa had drawn seven matches and won one since Blessin replaced Andriy Shevchenko in January.
Giovanni Simeone netted in the fifth minute as he just beat a defender to a through ball and poked it in at full stretch for his 16th league goal of the season.
Gianluca Caprari also saw a curled effort fingertipped onto the right post by Genoa goalkeeper Salvatore Sirigu.
Genoa remained three points from safety.
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