Siena, who started the season on minus six points for their involvement in a match-fixing scandal, moved off the bottom with their second win of the campaign.
Had they not been punished they would be joint-seventh with Fiorentina.
Striker Calaio, who has also played for Napoli, netted on 61 minutes after his long-range shot took a deflection.
His goalkeeper Gianluca Pegolo made several vital saves from the likes of Alberto Gilardino and Marco Motta.
Bologna sit 15th after the defeat, on four points.