The visitors made the breakthrough four minutes from time through Arturo Vidal, prompting a frantic final few minutes at Turin's Stadio Olimpico.
Torino defender Kamil Glik was sent off for a second bookable offence in the 90th minute, with Claudio Marchisio then grabbing a stoppage-time goal to seal the away win.
With just 12 points left to play for, the result moved Antonio Conte's side 11 points clear at the summit.
Torino had the first effort of the day when Alessio Cerci shot over from 25 yards before Juve took control.
Home goalkeeper Jean Francois Gillet punched away Stephan Lichtsteiner's cross but his clearance only found Mirko Vucinic, who shot high over the bar.
Paul Pogba then led a counter-attack and his pass back found Lichsteiner, who fired wide with the former's header then comfortably saved by Jean-Francois Gillet.
Gillet then easily gathered Lichtsteiner's shot from outside the box.
Juve goalkeeper Gianluigi Buffon was finally called upon in the last minute of the first half and was equal to an impressive effort by Mario Santana.
The match continued in the same vein on the resumption, with Vucinic's shot skimming the post and Pogba lashing wide.
Rolando Bianchi and Alessandro Gazzi fired over for Torino before Cerci put in a low cross from the left but it just evaded substitute Jonathas in front of goal.
With five minutes left, Pogba clumsily missed a great chance when he was picked out by Kwadwo Asamoah at the far post.
However, the visitors then went ahead a minute later. Marchisio found Vidal outside the box and he despatched his shot into the bottom-left corner with the goalkeeper well beaten.
Torino then found themselves down to 10 men with Glik sent off after a foul on Fabio Quagliarella which was deemed to be worthy of a second yellow card.
Juve sealed victory in stoppage time when Andrea Pirlo's free-kick found Marchisio unmarked in front of goal and he made no mistake.