The Robur began the new season with a six-point penalty - meted out for their involvement in match-fixing - but this victory allowed Serse Cosmi's men to leapfrog Palermo and Cagliari into 18th place.
Bologna coach Stefano Pioli was eventually sent to the stands for arguing with officials following an hour of heroics from Siena goalkeeper Gianluca Pegolo.
With two points on the board, Siena are now only three places shy of Pioli's Rossoblu, who have lost three of their first five games.
The touchpaper was lit on a feisty first half as Pegolo scraped Panagiotis Kone's rocket out from under the crossbar, the Siena keeper then left prone as Niccolo Cherubin glanced his header wide.
Alberto Gilardino was also unmarked as he met Mikael Antonsson's corner, but the former Parma man tamely nodded the ball against Pegolo to win a corner.
There was further drama in the Siena goal as Pegolo dived the wrong way to deal with Archimede Morleo's free-kick, just managing to twist his body in mid-air to flick the ball away with his trailing hand.
Siena came alive shortly before the break and Calaio was up in arms after being denied a clear chance on goal by the offside flag.
Pegolo had not switched off over the interval and proved as much as he repelled Marco Motta from close range when the game resumed.
Instead it was his opposite number, Federico Agliardi, who looked baffled as Calaio's 61st-minute strike ended up in his net thanks to a sizeable deflection from Antonsson.
Pioli was then sent to the stands for his over-zealous protestations as Gilardino was denied a penalty following minimal contact with Ze Eduardo in the Siena box.
The resolute Pegolo swept up Gabbiadini's long-range effort, with Sestu thwarted at the end of a fast break, but Siena had done enough to claim a second win of the season.