Their win on Saturday saw Inter move up to fourth in the Serie A standings.
Dejan Stankovic set the Nerazzurri on their way in the 20th minute and Diego Milito added a second 10 minutes later.
A brace from Samuel Eto'o in the second half put the result beyond doubt before Henry Gimenez grabbed a consolation for Bologna, who remain just four points clear of the relegation zone.
Milito's luckless season seemed set to continue when he headed against the outside of the post in the fifth minute.
Eto'o and Maicon also had good early efforts as Inter made a bright start.
They had to wait until the 20th minute to go ahead, and it was a controversial goal too as Stankovic received the ball from Eto'o in an offside position before he stroked it in, but the goal was allowed to stand.
Inter's second goal was also a dubious one, although Milito was only marginally offside when he latched onto the ball, beat Miguel Britos and then picked his spot in the far corner of Emiliano Viviano's goal.
The linesman's flag again stayed down, although more understandably so this time.
Marco Di Vaio was Bologna's main danger and he tested Luca Castellazzi in the 34th minute before Gimenez missed a chance to bring a spirited Bologna back into the game in the 51st minute.
Di Vaio's free-kick skimmed the post as Bologna searched for a way back into the game, but two goals in 10 minutes from Eto'o put paid to their hopes.
His first goal in the 63rd minute came from a neat one-two with Milito with the Cameroonian coolly slotting his shot into the far corner.
An unstoppable direct free-kick into the top left-hand corner in the 72nd minute then sealed the win for the home side.
Gimenez still wanted to end the game on a personal high and his shot was touched behind by Castellazzi.
The referee did not see the goalkeeper's intervention, whose honesty in ordering a corner backfired when Gimenez scored from the corner to earn a consolation for him and Bologna in the 77th minute.