Mauro Icardi scored both goals for the Nerazzurri, after six and 63 minutes, with Michele Pazienza's deflected shot bringing Bologna level first before Panagiotis Kone scored their second in the 74th minute.
Inter then missed a penalty late on, with Diego Milito denied from the spot.
The draw gives Inter a three-point advantage over sixth-placed Parma, who are in action on Sunday, while Bologna move two points clear of the relegation zone ahead of the remainder of the weekend's matches.
Luca Toni's second-half strike earned Hellas Verona derby honours from their clash with Chievo.
Leading scorer Toni slotted home the only goal of the game from close range in the 65th minute to follow up his brace in last weekend's 3-0 victory over Genoa.
The win at the Stadio Marc'Antonio Bentegodi keeps promoted Hellas well in the hunt for an unexpected European place, while leaving rivals Chievo still deep in trouble near the foot of the table.