The Italy international felt the reigning champions were back to their usual best and was pleased with his goal
The Old Lady had to settle for a 1-1 draw in their last league encounter, but bounced back with an impressive home-win over the Nerazzurri in Sunday's Derby d'Italia.
"We wanted to get back on track following our draw against Lazio and immediately handled the game in the right manner. It was a true Juve performance," Chiellini told reporters.
The Italy international was pleased with his goal as he made it 2-0 shortly after the break, yet stressed that Juventus should not have allowed Inter back in the game late in the second half.
"My goal gave us a bit of breathing space and it's always pleasing to score against Inter in such an important match.
"Inter's goal needs to serve as a lesson. It's not the first time we've run the risk of allowing opponents a way back into games we’ve already all but won and that can’t happen again in the future."
Juventus hold a nine-point lead over Roma in Serie A, but the Giallorossi have a game in hand.