Rudi Garcia's men were chasing Tottenham's European record of 11 victories from the beggining of the campaign, set in 1960-61, at the Stadio Olimpico di Torino and things were going to plan when Kevin Strootman gave them a half-time lead.
However, Alessio Cerci struck for the hosts after the break to ensure that his side left with a well deserved point.
The beginning of the match was a drab affair, but as time wore on Roma came closer and closer to breaking the deadlock, with set pieces proving a particularly big threat.
Alessandro Florenzi and Marco Boriello, the former with an ambitious volley, the latter with a header, both hit the top of the net following corners before the breakthrough arrived.
After Torino failed to clear their lines, the ball was worked to Miralem Pjanic, who picked outStrootman brilliantly, and the Dutch midfielder tucked the ball home emphatically.
However, rather than kicking on and taking the game by the horns, Roma eased off following the opener, allowing the hosts more and more of the ball.
Cerci had already sent a free kick in a decent position over the bar when he forced a great save from Morgan De Sanctis in the Roma goal with a bending shot from distance.
Torino pressed, but were ultimately unable to get back on level terms before the break.
Proceedings after half-time we much the same as the end of the first half and De Sanctis was once again called into action to soon enough to deny Riccardo Meggiorini, who met a fantastic high ball into the box with a volley that was beaten away by the veteran keeper.
However, it was not long before Giampiero Ventura's men got their deserved equaliser. Once again, Meggiorini found space on the left wing and squared it to Cerci, who duly steered it into the back of the net.
The equaliser spurred Roma into life and the Giallorossi soon went in search of another goal, with Nicolas Burdisso heading narrowly over from a header and Maicon having a tame appeal for a penalty turned down.
However, in the end, they could not craft a true chance and their winning start to the season came to an abrupt end.