The France international headed home a rebound from close range after Carlos Tevez had nodded Leonardo Bonucci's flick onto the bar, with replays suggesting that the Argentine striker was in an offside position.
Juventus dictated the tempo in a drab first half, with Claudio Marchisio coming closest on the stroke of half-time with a low drive.
But in the second half they turned their possession into a decisive goal thanks to Pogba's intervention.
Torino started with the league's joint top scorer Alessio Cerci leading their line, while Juventus restored Tevez to the starting XI after he was rested for the 2-1 victory over Chievo on Wednesday.
Juventus controlled the early possession but failed to create any clear-cut chances.
They almost found a breakthrough in the 14th minute when Sebastian Giovinco wriggled through several challenges on the right before delivering for Tevez, but the danger was snuffed out by a last-ditch clearance from Danilo D'Ambrosio.
As the hosts began to settle they won a series of set-pieces and they almost capitalised in the 26th minute when Cerci curled his 25-yard free-kick into the side netting.
Antonio Conte's side continued to look more threatening on the ball and Stephan Lichtsteiner's effort from distance curled wide.
Juventus could have stolen ahead in first-half injury time when Marchisio's 20-yard driven effort went narrowly wide of Daniele Padelli's post.
The visitors' pressure did not let up in the second half and Giovinco should have put Juventus ahead when a neat touch by Tevez left him one-on-one with the goalkeeper but he hit a tame effort straight at Padelli.
But Juventus deservedly took the lead in the 54th minute.
Bonucci headed a corner goalwards and Tevez somehow managed to head against the crossbar from two yards but the resultant rebound was headed home by Pogba. However, television replays suggested that Tevez may have been in an offside position.
Marchisio was lucky not to receive his marching orders 10 minutes later when he lunged into a tackle on Giuseppe Vives when already on a yellow card.
The hosts had a penalty shout waved away when Ciro Immobile went to ground under Giorgio Chiellini's challenge but referee Paolo Mazzoleni was unmoved.
Juventus almost grabbed a second in the 84th minute when Mirko Vucinic guided a back-post volley goalwards but Padelli parried away the danger.
Torino's fruitless run in matches against Juventus continues, with their last win against them coming in 1995.
