Massimo Maccarone twice put bottom side Siena ahead in Milan but two free-kicks from Wesley Sneijder, the second to equalise late on, and Walter Samuel's injury-time winner sent the Italian champions 11 points clear.
Inter's lead will be cut whatever happens in the meeting between second-placed AC Milan and third-placed Juventus in Turin on Sunday.
Siena took a surprise lead on 18 minutes when Maccarone was allowed to storm forward from the halfway line and fire in a 25-metre drive.
Inter were level soon after when striker Diego Milito, a revelation since his close-season move from Genoa, lashed in his 11th league goal of the season from a tight angle.
A textbook curling free-kick from Dutchman Sneijder put the hosts ahead on 36 minutes only for on-loan Juventus midfielder Albin Ekdal to sweep the ball home for Siena just moments later after arriving unmarked in the area.
Inter were without the suspended Mario Balotelli. Cristian Chivu and Esteban Cambiasso were among those injured while Cameroon's Samuel Eto'o was also absent at the African Nations Cup.
ROMA FOURTH
Defender Chivu fractured his skull in Wednesday's 1-0 win at Chievo and increasing crowd favourite Sneijder held up a shirt to the San Siro saying "Return soon Cris" after his first goal.
Midfielder Dejan Stankovic also limped off just as the second period was starting, leaving Inter without any real shape and they paid the price midway through the half when Maccarone netted his second from the edge of the area.
But by winning four Italian championships in a row, Inter have consistently shown they never give up and it was little surprise when Sneijder scored again on 88 minutes, this time using power to rifle in a free kick off the post.
Coach Jose Mourinho's record of 127 home league matches without defeat, including his time at Chelsea and Porto, was suddenly safe.
It got even better for the Portuguese when defender Samuel used all the skill of a striker to turn on the edge of the box and thump the winner deep into stoppage time.
"I am so happy. We really suffered but the win is so important," the Argentine substitute told Sky TV after ripping off his shirt in the rain and charging towards the corner.
In the early game, AS Roma moved back up to fourth after battling to a 1-0 home win over Chievo despite having goalkeeper Doni sent off on 11 minutes.
Daniele De Rossi headed in a corner in the first minute but Roma's hopes of victory looked to have suffered when Doni, only playing because of an injury to fellow Brazilian Julio Sergio, raced out of his box and handled Elvis Abbruscato's shot.
However, the hosts continued to have the best chances and new striker Luca Toni earned a penalty in the second half but David Pizarro, on spotkick duties with Francesco Totti again injured, saw his effort saved by Stefano Sorrentino.
