Two penalties and a header from the Chilean were enough to put FC Copenhagen to the sword despite former Juventus player Olof Mellberg scoring a hopeful equaliser in the second-half.
Vidal placed a powerful penalty beyond the reach of goalkeeper Johan Wiland on 27 minutes after the experienced Lars Jacobsen handled the ball just as Paul Pogba was about to latch onto a cross.
In a crazy eight minutes which saw Mellberg descend from hero to zero, FC Copenhagen equalised through the Swede before the hosts responded with two goals in three minutes, the former of which being a second penalty conceded by the centre-back.
The win means Juventus move to second position whilst their opponents fall to bottom of the group and it will be a battle for third place and a spot in the Europa League between themselves and Galatasaray who play Juventus in the ultimate game in Group B.
PRE-MATCH - Antonio Conte's side is boosted with the return of Girogio Chiellini to the heart of Juventus' defence. The Serie A champions haven't conceded a league goal in five games and the hosts will be hopeful of a clean sheet tonight.
27' - PENALTY: Jacobsen has handled the ball in the box. What a silly action.
28' - GOAL (Juventus 1-0): What a penalty from Vidal who hammers the ball into the bottom left hand corner beyond the reach of the goalkeeper.
41' - CHANCE: He gathers the ball on the edge of the box, curls an angled shot but the ball just bends around the post. Great effort.
55' - GOAL (Juventus 1-1): FC Copenhagen have equalise through former Juventus player Mellberg.
59' - PENALTY: Mellberg goes from hero to zero within minutes after taking down Llorente in the penalty area.
60' - GOAL (Juventus 2-1): Deja-vu! 2-1 to Juventus as Vidal once again scores emphatically from the spot.
63' - GOAL (Juventus 3-1): And it's a hat-trick for the Juventus star as he loops in a delightful header from a Pogba cross.
Juventus' shot conversion rate was 20%, the highest percentage for the Old Lady in a single game of this Champions League season.
The last Juventus player to score a Champions League hat-trick was Fillippo Inzaghi in September 2000.
Andrea Pirlo has made 97 UEFA Champions League appearances prior to tonight - the Copenhagen starting eleven had made just three more combined (100).
Copenhagen have now lost eight of their 10 CL away games, recording only one win and one draw.
Improved performance from Bianconeri: This was more like it from Juventus. They played with real conviction and, in truth, Antonio Conte's team should have won by more. Now with qualification in sight, can the Serie A champions finally deliver in the Champions League?
MAN OF THE MATCH
Arturo Vidal (Juventus): A faultless display. The Chilean scored two fantastic penalties under severe pressure and then sealed the deal with a looping header.
Juventus: Buffon 6, Caceres 5, Bonucci 6, Chiellini 6, Padoin 6, Vidal 9, Pirlo 8, Pogba 8, Asamoah 7, Tevez 7, Llorente 8. Subs: Marchisio 6, Vucinic 6, Ogbonna 6.
FC Copenhagen: Wiland 6, Jacobsen 5, Mellberg 7, Sigurdsson 6, Bengtsson 6, Bolanos 6, Delaney 6, Claudemir 7, Toutouh 6, Gíslason 7, Jørgensen 7. Subs: Amankwaa 6, Pourie 6.
THE MATCH IN A TWEET