After a tough opening period in which the Old Lady struggled to break the host side down, a piece of Vucinic magic helped create what turned out to be the winning goal.
An Alessandro Matri goal early in the second half was enough to give Antonio Conte a second consecutive win and move his side to the top of the Serie A table.
As well as securing all three points, the tactician will also be pleased with his side's character and resolve, despite its poor finishing on occasions.
The first half was a rather dour affair with little goalmouth action, which was mainly due to Siena's rugged defending and effective tactical set-up.
Matri and Andrea Pirlo both had unsuccessful attempts at goal, while Stephan Lichtsteiner was proving to be a threatening outlet down the right. But even he couldn't forge an opening, as the sides went in goalless at half time.
However, Conte's side managed to find a breakthrough just nine minutes after the break when Matri applied the finish to Mirko Vucinic's cut back.
The Montenegrin accepted a pass from Simone Pepe and then managed to weave his way through the Siena defense before expertly rolling the ball into the path of the Italy hitman to give Juventus the lead.
Their domination of possession almost counted for nothing on 68 minutes when Gaetano D'Agostino's pinpoint, curling free kick found the head of Emanuele Calaio, and the forward's header smacked the crossbar with Gianluigi Buffon beaten.
Even though the move was later adjudged to have been offside, the situation still served as a timely warning. Juventus consequently upped the ante, and Matri and substitute Arturo Vidal then had a great opportunity to put the result beyond doubt, but they both failed to make contact with Fabio Grosso's whipped cross from the left.
The Chilean was then played in all on his own minutes later, but he skied his shot high over the crossbar.
But, in the end, Juventus held out for the three points to continue the team's 100 percent record in Serie A.