Home debutant Innocent Emeghara, recently signed from Lorient, stunned the Nerazzurri with his first Siena goal only for Antonio Cassano to equalise inside 60 seconds.
It was a false dawn for Inter, though, as an Alessio Sestu goal ensured Giuseppe Iachini's men led their illustrious guests going into the break.
The second half might have been a different story for Inter had Cristian Chivu not seen red for a professional foul, with Alessandro Rosina converting the resulting penalty to settle the tie.
Emeghara gave Inter a taste of what he could do by setting Rosina through on goal, but the diminutive forward could not find the target.
The Nerazzurri looked to be in the ascendancy when Gianluca Pegolo sprawled to keep out efforts from Fredy Guarin and Juan Jesus, but it was not the case.
A fine counter-attack started by Rosina soon found Matteo Rubin to slam a low cross into the box, allowing Emeghara to get the fateful last touch.
Inter's response was immediate, though, as Yuto Nagatomo dummied a deceptive cross into Cassano's path. The ex-Roma man struck the ball hard and low beyond Pegolo and into the far corner.
The prompt response helped Inter to catch their breath, and in doing so they were caught out by a dynamic Siena side.
With 25 minutes played, Sestu made it 2-1 by wriggling free on the edge of the box before rifling the ball into the net.
Debutant Zdravko Kuzmanovic found a gap in front of Siena's backline to attempt an audacious equaliser, which missed its mark, but Inter had done enough to stay in the contest going into the break.
Chivu, however, made life harder for his side when play resumed.
The Romanian defender cut Emeghara down before he could convert Sestu's slide-rule pass, receiving his marching orders and allowing Rosina to beat Samir Handanovic from the spot.
Inter were now chasing down a two-goal lead with a one-man disadvantage but Cassano did not seem to care when he raced on to a spilled save from Pegolo to rattle the crossbar.
Siena would not be intimidated and both Rosina and Sestu came close to increasing their personal tallies with swift counter-attacking moves.
Inter head coach Andrea Stramaccioni had thrown deadline-day signing Mateo Kovacic into the fray at half-time and the promising Croatian playmaker attempted an audacious move in the 75th minute, only to overcomplicate things and lose possession.
That would be the last moment of promise for a poor Inter side, as Siena rode out a result that lifted them above Palermo and to within four points of safety.