The hosts dominated possession but lacked the finishing touch against a Chievo side that failed to test home goalkeeper Gianluca Curci until the 81st minute.
The outcome extended Bologna's unbeaten run to three games and handed the struggling visitors their first point in seven matches.
The hosts went into the clash on the back of two straight wins but failed to reproduce the form that saw them prevail 3-0 at Cagliari last time out.
Neither goalkeeper had a save to make in the opening half.
The home side were first to threaten in the 26th minute, when Jonathan Cristaldo got his head to Alessandro Diamanti's cross and his powerful effort went just wide of the far post.
The hosts picked up where they left off after the interval and wasted a fine opportunity to break the deadlock in the 56th minute, Panagiotis Kone latching onto Archimede Morleo's ball into the box but lashing a left-footed effort wide of the far post.
Cristaldo then went close with a bullet strike from 30 yards, but Puggioni produced a solid save.
On the hour mark, Frederik Sorensen met Diamanti's free-kick but could only direct his header harmlessly over the bar.
Puggioni kept out Davide Moscardelli's stinging 30-yard drive 12 minutes from time as Bologna continued to search in vain for the opener.
Three minutes later, Puggioni's opposite number Curci was finally given some work to do and was equal to the task of keeping out substitute Boadu Acosty's 12-yard left-footed shot, but both teams were running out of steam and settled for a point.