Chilean Vidal sent Stefano Sorrentino the wrong way after Mirko Vucinic went down easily under a clumsy challenge from Massimo Donati on 58 minutes.
They dominated the match but almost threw away the win at the death through poor defending as substitute Alejandro Faurlin's volley from close range was saved by Gianluigi Buffon.
Juve playmaker Paul Pogba soured proceedings late on by spitting at Salvatore Aronica and picking up a red card.
A draw would have been enough for the Bianconeri to clinch the title, on account of their head-to-head record, from Napoli.
It is the Old Lady's 29th title - although they held up a big sign on the pitch at the final whistle with 31 on it, signalling the two which were revoked following the Calciopoli scandal.
The Juventus Arena - which witnessed a pitch invasion at the final whistle - was jumping as the players emerged to a sea of flag waving and chants.
Kwadwo Asamoah was a menace from the left in the first half for Juve, beating men time and again but unable to find his team-mates with driven crosses while Andrea Pirlo sought to open up the away defence through the middle.
Sorrentino was the busiest man on the field. He blocked with his legs from Vucinic on the half-hour mark after the Montenegrin striker brought down a chipped pass and fired towards the near post.
Pirlo was given far too much time on the left to pick out a cross which had the keeper worried as Steve von Bergen out behind for a corner at the far post - but could easily have put through his own net.
For all their dominance, it was not until the second half that the real chances began to flow for Juve - but it was Palermo who first threatened, Fabrizio Miccoli firing a low strike from the corner of the box off the base of the far post.
Then came the penalty. Pogba picked out Vucinic with a chipped pass into the box and Donati, piling across to challenge, jumped into his back. Down went the striker, and the referee pointed to the spot.
Vidal made no mistake with the spot-kick - and Juve twice almost doubled their advantage soon afterwards.
First Asamoah crossed low for Vucinic at the far side of the box, whose centre was turned behind for a corner by Von Bergen with men arriving. Moments later Giorgio Chiellini, all alone a few yards out, contrived to head wide.
Pogba chipped another lovely ball into the area for Vucinic to turn a shot towards goal, saved low down by Sorrentino at the near post.
A rare attack at the other end saw sub Abel Hernández bend a strike just past the far post then Pogba almost lit up the match - the season, even - with a sublime piece of skill.
Juggling the ball on the right, he kept it up three times - knocking it past a defender with the third of them before sprinting around him and firing in a cross which almost led to a goal.
Two minutes later he was shown a red card as he responded to Aronica handing him off in the face with a gobful of words - then one of spit.
He left to standing ovation. Juve's fans put on a show late on, the entire stadium waving their free flags in a flurry of black and white - but their thunder was almost stolen away by Faurlin.
Sorrentino sent a long ball forward and confusion reigned on the edge of the box, allowing the former QPR midfielder to meet it with a volley.
Home captain and legend Buffon did his job with a block to seal the three points for the Bianconeri.
- Sports & Recreation
- Mirko Vucinic
- Stefano Sorrentino
- Paul Pogba
- Gianluigi Buffon
- Massimo Donati