Juventus keep perfect Serie A record
Summer signing Pogba had seen an earlier effort harshly ruled out but had the final say when he nodded Sebastian Giovinco's cross past a hesitant Federico Agliardi.
Bologna had battled bravely and looked like they might grab a point when Saphir Taider cancelled out Fabio Quagliarella's opener with 16 minutes left.
But Juve were completely dominant in the final minutes before Pogba grabbed his winner to move the Turin club four points clear after Napoli, who began the night in second place, lost at Atalanta.
Juve's 1-0 win over Catania at the weekend was shrouded in controversy with replays suggesting Arturo Vidal's winner was offside after the hosts had an earlier effort ruled out.
It was Juve who were this time left aggrieved in a frustrating opening 45 minutes as the referee's whistle denied Pogba.
The former Manchester United midfielder rose to head in a corner but his celebrations were cut short when the referee ruled he had pushed Marco Motta.
Pogba was proving a menace early on and moments later he cracked a curling shot against the upright.
Bologna had the ball in the net themselves on 18 minutes but the referee had already blown for an early infringement.
Juve had chances to go into the break ahead but Nicklas Bendtner saw a long-range effort tipped wide before Pogba headed over.
Pogba provided the pass to fire Juve ahead on 53 minutes when he picked out Quagliarella who poked into an empty net. Quagliarella almost had a second moments later but Agliardi saved well.
Bendtner then shot wide and Juve looked like they might be made to pay when Taider smashed in an equaliser from outside the area.
Juve poured on the pressure thereafter, with Andrea Pirlo fizzing a corner just over, before Pogba won it after Giovinco's perfect cross picked him out.