Pogba decided a hard-fought encounter 13 minutes from the end when he was quickest to the ball after Fabio Quagliarella's long-range effort crashed back off the crossbar.
The Frenchman still needed to keep his cool to beat Parma goalkeeper Antonio Mirante and secure a third win on the spin since Juve were beaten at the Bernabeu a fortnight ago.
That reverse has left Antonio Conte's side in grave danger of missing out on the knockout stages ahead of Madrid's arrival in Turin this week.
Despite the importance of that match, Conte named a near full-strength side - with Andrea Pirlo and Quagliarella the most notable names on the bench - although the Italy internationals were needed to be called upon before Pogba was able to finally end Parma's resistence.
Juve's win moved them two points behind leaders Roma, who Conte and his staff can watch close up on Sunday when they travel to Torino.
The champions had to weather an early storm as Amauri twice went close before Massimo Gobbi slid a pass across the face of goal that a backtracking Giorgio Chiellini did well to avoid at the back post.
Juve tested Mirante for the first time when Carlos Tevez played a one-two with Giovinco - who returned the ball via a backheel - but the defence closed in and Tevez forced a shot straight at the keeper.
Arturo Vidal then flashed a low shot just wide of a diving Mirante while Amauri lashed high over at the other end.
Juve's search for a winner after the break was initially frustrated by Mirante who clawed another Tevez effort out of the corner following more good lead-up work from Giovinco.
The diminutive forward then himself shot over before another athletic Mirante save denied Tevez.
With time ticking down it appeared Parma might hold out for a point only for Pogba to strike.
Substitute Quagliarella's stunning 25-yard shot crashed off the crossbar and, while Mirante recovered after initially being wrong-footed, Pogba kept his cool to steer the ball beyond him and grab victory.