Antonio Conte's men initially suffered frustration against their struggling opponents at Juventus Stadium on Saturday, before Pogba found the breakthrough in the 64th minute.
Regardless of other results, Juventus can guarantee a third straight domestic crown with wins over Sassuolo and Atalanta before they visit second-placed Roma on May 9, while the reigning champions could even retain the Scudetto sooner should Rudi Garcia's side slip up.
Pogba saw two promising chances go begging within the first quarter of an hour, but from there Bologna kept things tight with a solid defensive display.
That trend continued after the break, but Pogba ultimately found a way through to ease the tension in Turin.
The result was somewhat harsh on Bologna, who sit just one place above the drop zone - level on points with 18th-placed Sassuolo - and must quickly regroup ahead of a home game against Fiorentina next weekend.
Juve carved open the visiting defence as early as the fifth minute. Fernando Llorente held the ball up well before laying into the path of Pogba, who sent a tame shot straight at goalkeeper Gianluca Curci when he should have done better.
Pogba was once more guilty of wastefulness from Juve's next opportunity, the France international heading Andrea Pirlo's superb corner over the crossbar from eight yards.
Having survived those early scares, Bologna improved at the back and restricted the home side to a series of fruitless crosses, although Juve may have moved ahead had Claudio Marchisio made contact with Llorente's centre shortly before the half-hour mark.
Llorente had tentative claims for a penalty turned down soon after when he claimed Bologna centre-back Mikael Antonsson had tugged his shirt.
The Spaniard appeared to go to ground too easily and referee Piero Giacomelli waved play on.
Juventus looked for more thrust in attack after the break, and a neat flick from Sebastian Giovinco found its way to Mauricio Isla – playing in place of the suspended Stephan Lichtsteiner - but Curci was quick to react and made a smart save.
Juve's frustrations continued as Pogba curled a left-footed shot from the edge of the box wide of the far post.
Pogba was not to be denied, however, and finally broke Bologna's brave resistance in the 63rd minute.
The France international received Isla's pass before drilling a low effort into the bottom left-hand corner.
From the next attack Isla almost doubled the lead but he was denied as Curci sprung to his left to make a stop.
Pogba again went close in the closing stages, the 21-year-old hitting a half-volley straight at Curci from eight yards.
However, one goal proved to be enough for Juventus, who can now look forward to Thursday's encounter at Benfica in the first leg of a UEFA Europa League semi-final.
