An Andrea Belotti volley in the second half cancelled out Matthijs de Ligt's early header, leaving Juve fourth in the table on 47 points after 26 games, eight behind leaders AC Milan, who visit bottom side Salernitana on Saturday.
Juve are already missing highly experienced centrebacks Giorgio Chiellini and Leonardo Bonucci through injury, while midfielder Federico Chiesa is out for the rest of the season after tearing knee ligaments in January.
Dutch defender De Ligt headed Juve in front in the 13th minute, arriving at the far post to connect with a Juan Cuadrado free kick.
Torino coped well with falling behind and matched their more illustrious neighbours for intensity and intelligence and went on to outplay them in the second half.
After coming close to scoring on a few occasions they found an equaliser when Josip Brekalo raced to the byline and launched a cross back into the box which star striker Belotti converted on the volley.
Torino continued to cause the hosts problems until late in the game but were forced to defend with their backs against the wall deep in stoppage time before they could celebrate a well-earned point, taking them on to 33 points in 10th place.
"We had two or three chances in the first half but not many in the second, when we didn't play with as much freedom. Sometimes that can happen and at least we took a point," Allegri told DAZN.
"The draw allows us to continue the positive results we've had in the last three months," added the Juve coach, whose side extended their unbeaten run in the league to 12 games, having lost five of their first 14.