The Bianconeri knew that failure to condemn Fiorentina to a third straight away defeat would leave the door open for Napoli to close a three-point gap with any points earned at Lazio.
Juve boss Antonio Conte had played down talk of a fierce rivalry between Turin and Florence and there was precious little evidence of competition on the pitch as Vucinic was left unchallenged to slam home the opener.
Matri lost his boot when swinging at Arturo Vidal's canny pass but his socked foot guaranteed Juve all three points before what turned out to be an insipid second half.
Stevan Jovetic let rip with a fine left-footed effort inside 60 seconds but the first half would belong to Juventus.
Andrea Pirlo was back to his imperious best, with a series of deft balls forward to Vidal and Claudio Marchisio inspiring gasps from the bumper crowd.
Juve's first shot on goal came through Marchisio, who dribbled to the edge of the area before directing an effort just wide, before Emiliano Viviano was called into action.
With Vucinic free to do as he pleased at the end of an attractive passing move, the Montenegrin rifled the ball against Fiorentina's goalkeeper.
Vucinic's compatriot Jovetic soon warmed Gianluigi Buffon's palms on the turn but it would be Juve who made the breakthrough.
With 20 minutes played Vucinic unleashed a furious right-footed drive that streaked past a stranded Viviano and into the net.
A chance for a quickfire second went begging when Vucinic failed to tuck the ball away when Gonzalo Rodriguez offered it to him on a plate at the edge of his area
Juve would give themselves a significant advantage going into the break, though, as Matri stole onto a Vidal pass to steer the ball past Viviano.
Replays showed the former Cagliari man's boot had flown off before he scored with his sock.
Pirlo went close himself when play resumed, just before Marchisio and Federico Peluso picked up the bookings that will keep them out of next week's trip to Roma.
It was then time for Sebastian Giovinco to make an entrance when Vucinic called to be replaced after crashing to the ground and hurting his knee.
Matri shrugged off the lull in action to burst onto a Stephan Lichtsteiner pass and drag the ball just wide of a post.
Fiorentina substitute Mounir El Hamdaoui got Buffon working again when he twisted and turned to beat Peluso and Giovinco promptly drew a low save from Viviano at the other end.
But after the high-tempo escapades of the first 45 minutes, the second half was a limp affair and not even Paul Pogba could liven things up with one of his trademark long-range screamers.
The Frenchman looked up and shaped himself to shoot but opted instead to pass sideways to Marchisio, who could not quite dig out one last meaningful effort on the half-volley.