The league leaders broke the deadlock in the 19th minute, when Vucinic cannoned home a shot from outside the penalty area to put Juve ahead.
The hosts then doubled their lead just minutes before the break, as Arturo Vidal drove forward at the Viola defence before picking out Matri, who guided the ball past Emiliano Viviano to make the score 2-0.
Andrea Pirlo had a chance to add a third eight minutes into the second half, but his 35-yard effort flew over the bar.
Matri came close to grabbing his second of the night with 23 minutes left to go, but he fired his effort just wide after receiving a cross from Stephan Lichtsteiner.
The win temporarily extends Juve's lead at the top of the table to six points, while Fiorentina stay sixth.