The Bianconeri came into the weekend unbeaten and just two points off leaders Roma - who were in action later on Sunday - and kept up the pressure thanks to Pogba's second-half header.
Torino, without a win over Juve since 1995, never looked in danger of breaking that unwanted record and produced few chances of merit over the 90 minutes.
Pogba had the first opportunity in the 15th minute when his effort from distance was held by Daniele Padelli, and the visitors continued to dominate for the remainder of the half with Sebastian Giovinco and Claudio Marchisio both spurning presentable openings.
Giovinco had another good sighting six minutes into the second period when he was played in by Carlos Tevez but saw his low driven effort saved by the feet of Padelli. The ball then broke to Kwadwo Asamoah but his shot deflected for a corner.
Juve continued to apply the pressure and it was from another corner in the 54th minute that they made the breakthrough.
The set-piece was flicked on for Tevez who should really have scored from a yard out but saw his header come back off the bar, but Pogba spared his team-mate's blushes as he stooped to nod in the rebound.
Juventus remained the only team likely to add to the scoring in what time remained, and with 84 minutes on the clock they were only denied a second when Padelli got across smartly to his left to palm away Mirko Vucinic's volley.