The Serie A side moved up to second in the group with the win and now know that a draw away to Galatasaray in a fortnight's time will be enough for them to reach the second round.
"Scoring three goals is a dream," Vidal, who hit all three of his side's goals, told UEFA.com. "Today is an important day for me but also for all the Chilean people in the world.
"The most important thing, however, is that we won and took another step towards qualification. This is a tough group but if we play at our level, we will be able to progress.
"Tonight we played well, with confidence, and in the end we managed to achieve what we wanted: three points."
The win was Juve's first in the Champions League this season.