The Nerazzurri were on the backfoot at the start of the encounter, as the hosts could have scored on four occasions inside the first 20 minutes.
Diamanti fired just wide of the Inter goal in the 12th minute and then saw his dangerous cross intercepted by Samir Handanovic.
Andrea Ranocchia came agonisingly close of putting Inter in the lead midway through the first half when he headed a corner just inches wide of the mark.
However, five minutes later the central defender did find the target; this time heading home Esteban Cambiasso's free kick.
Bologna should have equalised just seconds after the restart when Gilardino sent through Manolo Gabbiadini on goal, but the youngster failed to keep his shot on target.
Five minutes later the home side pulled one back when Nicolo Cherubin headed home Diamanti's cross past a helpless Handanovic after getting in front of Ranocchia.
However, minutes later Inter restored their two-goal advantage and wrapped up the win, as Cambiasso chipped an intelligent Palacio ball over Federico Agliardi.