Alessandro Diamanti curled in a stunning free-kick in the 54th minute for the only goal of the game.
It means that Bologna are now six points above the relegation zone in 12th position with just six games remaining.
Cagliari are in 14th place on 38 points but just four points ahead of Lecce who currently hold the third and final relegation spot in 18th.
The match came alive in the second half after a drab opening period.
Cagliari pushed hard for an equaliser after going behind with Andrea Cossu and Thiago Ribeiro coming close before Joaquin Larrivey hit the crossbar.
Both teams also needed their goalkeepers to make a number of good saves to keep the score as it was.
Bologna next travel to face Siena on Sunday while Cagliari host Catania next Monday night.