Juve have endured a tough start to the season under new boss Massimiliano Allegri, sitting 10th in Serie A, but they put that behind them in Europe.
Juve were content to allow Chelsea to hold possession throughout the first half, with Thomas Tuchel's men enjoying 72% of the play in Turin. But despite dominating the ball, Chelsea struggled to create chances and open up the home side.
The only shot on target for either side in the opening 45 minutes came from Romelu Lukaku, who hit a left-footed effort tamely at Wojciech Szczesny from Marcos Alonso's corner routine after just seven minutes.
The best opening for the home side came for Chiesa, with the forward expertly turning Antonio Rudiger and bursting into the box before dragging a shot wide of Edouard Mendy's far post.
But it was Juve who scored the first goal of the game -- and it came just 10 seconds after the restart. Federico Bernardeschi fed Chiesa inside the area, and the striker lifted his shot expertly into the roof of the net.
Juve should have made it two when Adrien Rabiot cushioned a ball across the box into the path of Bernardeschi, but he somehow fired over the bar with the goal at his mercy.
Chelsea almost snatched a 95th-minute equaliser but Kai Havertz headed over the bar.
Afterward, Tuchel said he felt his side had lost their mental sharpness even before the Champions League holders stepped on the pitch.
"We had a very good training session yesterday," Tuchel told reporters. "We were absolutely sharp and looked very fresh and very hungry, ready for bounce back [from defeat to Manchester City].
"I think it's very difficult to find rhythm against a team that defends so deep, it was completely the other way around in the Manchester City game.
"The big difference was that we gave big mistakes away that cost us confidence. Early today I could tell it was different. We were not as fresh mentally as we were in training yesterday. I don't know why."
Tuchel's team did not have a single attempt on target against City at the weekend, but the German insisted he is not worried by their lack of attacking threat.
"We were lacking runs, we were struggling to find our rhythm and to keep the belief structure," Tuchel added.
"Maybe it is a shooting problem, because if you don't shoot then you don't score. But if you play against a team that sit so deep like today it is hard to take shots. We will learn."
The win over Chelsea was Juve's third win in a row in all competitions, as the Serie A team moved onto six points at the top of Champions League Group H.
"Usually sailors always find the way out when they are in a storm," Allegri said. "Tonight we played a good match against the European champions.
"There is no turning point, let's just take the six points and be happy. The [league] championship is another thing.
"Tonight the team understood that against another side who do not allow you to have possession, you have to adapt and have a defensive match. I never got angry, the defending was perfect."