Vucinic came off the bench for the second half to score and also earn a penalty.
"One man does not change a game," Vucinic told the official Juventus website.
"It is the group that came out and fought back, as we have done so many times. It was a victory from the team.
"We went behind twice against a strong side, but recovered the situation with character. We start the season on the right foot.
"I want to dedicate the victory to the Juventus fans and my family, while of course we are also happy for Antonio Conte."