In a largely one-sided game, Vucinic struck twice to see off the challenge of a Pescara side who found a consolation through Emmanuel Cascione's stunning effort.
The win lifts Antonio Conte's side 12 points clear of Napoli at the top of the table, and warms them up for Wednesday's Champions League quarter-final tie with Bundesliga champions Bayern Munich.
With one eye on Bayern, Conte left the likes of Gianluigi Buffon, Andrea Pirlo and Fabio Quagliarella on the bench, but the changes did not seem to take anything away from the dominant force in Serie A.
The game was dominated from start to finish by the Bianconeri who, try as they might, could not break the deadlock before half-time.
Pescara had goalkeeper Ivan Pellizzoli to thank for keeping them in the game at the interval as he made numerous fine saves, the first from Emanuele Giaccherini in the 12th minute.
Pellizzoli then turned Quagliarella's shot on to the post after Sebastian Giovinco had been forced to leave the field injured.
Another fine one-handed save from Pellizzoli denied Giaccherini once again just a minute before half-time.
Vucinic missed a glorious chance to open the scoring five minutes into the second half but he still proved decisive with his next two attempts.
A foul on Arturo Vidal by Giuseppe Rizzo earned the Pescara midfielder a red card and Juventus a penalty in the 72nd minute, and Vucinic stroked the ball home to put the hosts in front.
Vucinic made it two a few minutes later, picking his spot in the far corner before heading off the pitch for a deserved rest as Conte sent on Alessandro Matri.
Matri wasted the chance to make it three when he dragged a shot wide of the post and Juve were made to sweat for the last seven minutes when Cascione curled an unstoppable 20-yard effort into the top-right corner of Marco Storari's goal.
It was Pescara's first shot of the game and, although they tested Storari with another goalbound effort before full-time, Juve held on to take all three points and edge closer to a second successive Serie A title.