The away goalkeeper was called into action again twice before the break when he kept out efforts from Alessandro Diamanti and Acquafresca.
Bologna netted the winner in impressive style 10 minutes into the second half thanks to Diamanti's pinpoint free kick.
Andrea Cossu nearly found an equaliser minutes later, but his shot was saved following Agazzi's long punt upfield.
The hosts pushed for a second goal to put the game to bed, but again Agazzi was equal to Acquafresca's attempt.
The win has lifted Bologna up to 11th in the table, while Cagliari stay 14th.