After dropping the two precious points Stefano Pioli's side hold a slender lead over second-placed Napoli, who ran out impressive 3-1 winners at Atalanta on Sunday afternoon.
Defending champions Inter Milan are four points back in third with a game in hand following their 1-0 triumph at fourth-placed Juventus, who are eight points off the pace with seven matches left.
The draw was another disappointing result against one of the league's lesser lights, their displays against teams they should beat a consistent problem as the season heads towards its climax.
Bologna, who sit 12th, were without their coach Sinisa Mihajlovic who is being treated for leukaemia but spoke to his players on a video call from Sant'Orsola hospital in the northern Italian city.
The away side fought throughout in front of over 68,000 fans at the San Siro and could even have taken the lead midway through the first half when Mike Maignan pulled off a fingertip save to keep out Musa Barrow's long-range rocket.
However Milan dominated the play as they pushed to maintain their three-point lead on Napoli, with Olivier Giroud being denied twice just before half-time by Lukasz Skorupski.
The hosts came out aggressively after the break but again struggled to find away past Skorupski, who kept out Rafael Leao's low drive before watching Davide Calabria's 61st-minute drive fly just wide after being set up by his Portuguese teammate.
Leao scuffed wide a curling effort 11 minutes later and Fikayo Tomori hooked over the bar before Skorupski saved a point for Bologna in the fifth minute of stoppage time by tipping over Ante Rebic's powerful header, which fortunately for the Pole was hit straight down the middle of his goal.
Earlier Giovanni Simeone struck his 16th league goal of the season in Verona's 1-0 win over relegation-threatened Genoa who fell to their first defeat under coach Alexander Blessin.
Simeone became only the second player in Verona's history after Luca Toni to net more than 15 times in a single Serie A campaign after his decisive fifth-minute strike which moved Verona up to ninth and left Genoa second from bottom, three points from safety.
Blessin had not lost in his previous eight matches in charge since arriving at Genoa a virtual unknown in January, running out seven consecutive draws before beating Torino just before the international break.
Verona were playing without the support of their hardcore fans after the Curva Sud section of the Stadio Bentegodi was closed following racist abuse directed at Napoli's Kalidou Koulibaly and Victor Osimhen in their previous home fixture last month.