Antonio Conte's men headed into this Group B clash knowing their margin for error was getting smaller and that a failure to win could leave progression out of their hands or even off the table.
That was looking as though it could be the case too when former Juve defender Olof Mellberg cancelled out Vidal's first-half penalty.
Mellberg would change the game again shortly after, though, giving away another penalty which Vidal tucked away before completing his hat-trick.
The outcome is that Juve head to Galatasaray in the final group game knowing they can guarantee qualification with a win and, considering Copenhagen next face Real Madrid, could well do so with a draw.
Juventus were not to know how the night would unfold, though, and were keen to dictate the pace from the off owing to their situation and Paul Pogba registered a sixth-minute effort which Johan Wiland dealt with.
Copenhagen hit back with Mellberg heading wide when well set and Youssef Toutouh drawing a save out of Gianluigi Buffon.
The home side could have done without some time on the back foot but managed to get back on top and Mellberg did well to block a Carlos Tevez effort.
Pressure would tell in the 28th minute as Andrea Pirlo's ball into the box was handled by Lars Jacobsen and Vidal did the rest from the spot.
The same man went after a second and worked Wiland from range, before Pogba flashed a strike just wide as the interval approached.
Knowing one goal may not be enough, the second half started with Juve piling forward as Tevez again threatened the goal.
Kwadwo Asamoah then took aim only to find Mellberg a willing blocker again, before the Swede produced an even more telling contribution at the other end.
Fifty-six minutes were on the clock when Mellberg pounced on Ragnar Sigurdsson's knock-down to crack in an equaliser that left his former fans stunned.
Salvation was close by for them, though, on what was a mad night for Mellberg.
Three minutes later he was late on Fernando Llorente in the box and after a penalty was given, Vidal repeated his earlier trick.
He ensured there would be no repeat of Mellberg's equaliser too when, just four minutes later, he arrived on to a Pogba cross to head in a fine hat-trick third.
Pogba's general play were perhaps worthy of a goal and he had a late piledriver charged down, but it did not matter by that stage.