The result brings to an end Roma's record run of 10 consecutive league victories, with Rudi Garcia's side now three points clear of Napoli and Juventus, the two teams immediately behind them in the table.
Kevin Strootman had put Roma in front after 28 minutes, sweeping home Miralem Pjanic's cutback after Torino had failed to clear a corner properly.
But the hosts hit back 18 minutes into the second half through Alessio Cerci, just the second goal that Roma have conceded in a remarkable start to their league campaign and first in a staggering 743 minutes.
Leaders Roma pressed hard for a winner in the final stages with a succession of dangerous free-kicks in and around the Torino area, but the home side stood firm to claim their fourth league draw in five matches.
Earlier in the day, fourth-placed Inter extended their unbeaten run to four matches with a comfortable 3-0 success away at Udinese.
Rodrigo Palacio gave Walter Mazzarri's side the lead with a firm header on 25 minutes, before Andrea Ranocchia volleyed home his first goal of the season four minutes later to double Inter's advantage.
Palacio then set up Ricardo Alvarez in second-half stoppage-time as Inter maintained their unbeaten record away from home this season.
Verona are a place behind Inter on goal difference following their 2-1 home win over Cagliari.
Luca Toni, playing in his 500th domestic match, scored his 225th goal after eight minutes before that advantage was doubled by Bosko Jankovic 12 minutes into the second half.
Daniele Conti did pull one back for the visitors right at the end, but it was not enough to deny Verona a fifth win in six, while Cagliari have now won just once since the opening day of the season.
The game of the day came between two of the division's struggling sides, as Sassuolo won 4-3 away at 10-man Sampdoria.
Domenico Berardi was the star, scoring three of Sassuolo's four goals to become the second youngest player, at 19 years and 94 days, to score a Serie A hat-trick this century, second only to Bari's Francesco Grandolfo, who claimed a treble versus Bologna in May 2011 aged 18 years and 300 days.
Nicola Pozzi had given the hosts the lead in the 19th minute before Berardi claimed his first four minutes after the break.
Sampdoria then saw Andrea Costa sent off for a second caution in the 52nd minute, Berardi tucking away the resulting penalty before Antonio Floro Flores added another 11 minutes later.
The hosts pulled one back almost immediately through Eder and Lorenzo De Silvestri looked to have rescued a point with his strike nine minutes from time, only for Berardi to take centre stage once more and net the winner from the spot with just two minutes remaining.
Elsewhere, second-half goals from Juraj Kucka and Alberto Gilardino saw Genoa win 2-0 at Lazio, while Paulinho's 11th-minute strike handed Livorno a 1-0 home win over Atalanta, who saw Carlos Carmona sent off 10 minutes before half-time.
