Rolando Bianchi gave Torino the lead with a header just after the break before defender Nicolas Burdisso nodded the equaliser for the champions, who piled on the pressure in the closing stages and hit the post twice.
Inter's lead remains six points after Milan moved above Juventus with a 3-0 win at Lazio in the late game.
Since the mid-season break, Inter have drawn with Cagliari, been easily beaten at Atalanta, scraped a win at home to Sampdoria and played well in Wednesday's 2-0 victory at Catania.
Hernan Crespo and Zlatan Ibrahimovic hit the woodwork in a frantic finish and Inter substitute Ricardo Quaresma, heckled by his own fans, spurned a great chance. Torino's Ignazio Abate was also lucky not to concede a penalty for handball.
"I never like drawing at home but I accept it. We created lots of chances but Torino defended with a fantastic spirit," Inter coach Jose Mourinho told Sky as he bemoaned Sulley Muntari's suspension and Dejan Stankovic's first-half injury.
Genoa remain fourth thanks to Domenico Criscito's 88th minute goal in a 1-0 home win over Palermo.
Striker Bernardo Corradi put the hosts ahead with a penalty but a David Pizarro brace gave Roma the lead before Francesco Cozza capitalised on Simone Loria's mistake.
All Italian games this weekend kicked off 15 minutes late because of a protest over the Court of Arbitration for Sport banning Napoli's Daniele Mannini and Brescia's Davide Possanzini for a year for being late for a 2007 drugs test.
