The Inter goalkeeper did well to smother a drilled Arnautović shot shortly afterwards, while at the other end, Jhon Lucumi blocked Edin Džeko’s goalbound effort.
However, Bologna took the lead completely out of the blue midway through the first half as Riccardo Orsolini’s 30-yard volley cannoned off the back of Charalampos Lykogiannis to leave Onana wrongfooted and the home faithful stunned.
However, Lykogiannis was on the wrong end of a deflection minutes later as Denzel Dumfries’ cross clipped the left-back and looped up in the air for Džeko to slam in a jaw-dropping volley.
The comeback was soon complete when Lucumi was booked for a challenge on Lautaro Martínez, with Federico Dimarco stepping up to curl home the free-kick from 20 yards.
Džeko somehow failed to double his tally for the evening almost immediately after the interval when he headed Dumfries’ sumptuous cross against the bar from a few yards out, but that quickly ceased to matter as Dimarco produced a neat turn to outfox the recently introduced Joaquín Sosa before whipping into the far corner.