Both clubs had claimed maximum points from their opening two matches, but Inter have looked the more confident side under new boss Walter Mazzarri, who arrived from runners-up Napoli.
Indeed it was the home side who broke the deadlock midway through the second half at San Siro as substitute Mauro Icardi scored his first goal in Nerazzurri colours, but Chilean midfielder Vidal - already a two-time Scudetto winner with Juve - responded with his 20th league goal for the Turin giants.
The leaky backline that took a large chunk of the blame when Inter finished in a lowly ninth place last season had not conceded a goal in two league games under Mazzarri and impressed again.
Hugo Campagnaro cut out a cool through-ball from Carlos Tevez in the opening exchanges before goalkeeper Samir Handanovic dashed onto a cross from Paul Pogba.
Inter's frontline has also looked more intimidating and Yuto Nagatomo went close to notching a sixth Nerazzurri goal of the season, only for visiting keeper Gianluigi Buffon to protect his nets.
At the other end Andrea Pirlo's free-kick sailed straight down Handanovic's throat before Juve clamoured for a penalty in the 18th minute.
Vidal was on the ground in the box but referee Gianluca Rocchi instead whistled for a handball.
On the 30-minute mark Pogba connected poorly with a left-footed volley under the posts, Handanovic parrying with ease, and Juve had wasted their best chance of the half.
Inter's came a few minutes before the break as Pirlo lost possession in midfield, but Saphir Taider's ambitious finish at the end of a counter-attack was repelled by the alert Buffon.
A slower start to the second half saw Rodrigo Palacio test Buffon with a header before Vidal messed up his finish from a neat Tevez pass.
Fredy Guarin rattled the crossbar with a right-footed shot and, with Mazzarri looking increasingly frustrated on the touchline, he threw Icardi into the action for Taider.
That move paid immediate dividends as the young Argentinian opened his Inter account in the 73rd minute.
A lapse in concentration from Giorgio Chiellini allowed Ricky Alvarez to steal the ball on the right. He fed Icardi on the edge of the box and the summer signing from Sampdoria clipped over Buffon to inspire rapture in the San Siro crowd.
Hush descended two minutes later, though, as Vidal dug out a left-footed finish to equalise when standing unchecked in Handanovic's box.
Tevez and Pogba both came knocking in the final throes but it would be Mauricio Isla who missed the clearest chance to turn the game on its head.
With two minutes remaining, Tevez's cross from the by-line found Vidal, whose bullet header sent Handanovic sprawling only for Isla to slice the loose ball past the near post and into the stands.