The midfielder scored in the first half before the Italy international netted a late clincher after the champions had spurned a number of chances to make the points safe
Antonio Conte's men went into the clash three points ahead of Roma at the summit following a run of six straight league wins.
The defending champions have not tasted defeat in Bologna since 1998, and made sure of another three points at the Stadio Renato Dall'Ara with a highly professional performance.
Midfielder Vidal opened the scoring in the early stages with a close-range effort as Juve dictated the first half.
Bologna did threaten sporadically after the interval, but their hopes of taking a share of the spoils were killed off when Chiellini struck in the final minute of normal time.
Juventus made six changes to the side that overcame Udinese last time out, with Paul Pogba, Mirko Vucinic and Fabio Quagliarella among those recalled in place of Andrea Pirlo, Carlos Tevez and Fernando Llorente.
There were two alterations to the Bologna team that drew with Parma in their previous league encounter, one of which saw Andrea Mantovani replace the suspended Frederik Sorensen in defence.
The visitors dictated play during the early stages and deservedly took the lead after 12 minutes, Vidal latching on to Federico Peluso's ball over the top to volley home moments after Claudio Marchisio had seen a goalbound effort cleared following another sparkling Juve move.
Conte's men looked to kill off the game and came close to a second five minutes later when Quagliarella had an effort deflected wide.
Attacking midfielder Alessandro Diamanti twice tested Buffon from range as Bologna looked to find a way back before half-time, but Juve's defence was rarely troubled.
Juventus began the second half with renewed energy and came close to doubling their advantage just after the break when Marchisio curled wide from a tight angle.
Bologna struggled to find a foothold in the game and goalkeeper Gianluca Curci needed to be at his best when twice pulling off superb saves to deny substitute Llorente.
Curci was beaten for a second time after 67 minutes, but Kwadwo Asamoah was adjudged to have been offside as he collected Llorente's neat throughball.
Despite Juve's clear superiority, Bologna should perhaps have levelled when striker Jonathan Cristaldo fired narrowly wide of the far post following an excellent counter-attack.
Marchisio and Llorente spurned further chances as the game headed to its conclusion, while Archimede Morleo headed over for Bologna.
The game was finally ended as a contest in the dying stages, Chiellini converting at the near post from a Carlos Tevez corner.