Juventus, last season's beaten Champions League finalists, meet City in their Group D opener on Tuesday and on this showing Manuel Pellegrini's men will fancy their chances of taking three points off the Italian champions.
Having already suffered their worst ever start to a Serie A season following defeats to Udinese and Roma, Juventus welcomed Chievo to Turin determined to take all three points, albeit with one eye on Tuesday's fixture.
Coach Massimiliano Allegri left Juan Cuadrado, Mario Mandzukic and Paul Pogba on the bench and handed full debuts to former Inter Milan midfielder Hernanes as well as Brazilian defender Alex Sandro.
The trio's presence, however, was eventually required as Juve fought in vain to level after conceding a fifth-minute opener when Perparim Hetemaj fired low past Gianluigi Buffon from outside the area.
Buffon would hold his finger to his lips in a bid to silence Juve's fans at half-time as the hosts were whistled and jeered off. Before then, Juve had spurned a few real chances to pull level, and perhaps overtake the Flying Donkeys.
Hernanes, impressive throughout playing just behind Dybala and Alvaro Morata, notably stung Albano Bizzarri's gloves with a superb drive, while Leonardo Bonucci and Roberto Pereyra both missed half-chances.
After several weeks out through injury, the still rusty Claudio Marchisio was replaced by the more effective Pogba at half-time and although the later introduction of Juan Cuadrado improved Juve's prospects further, Chievo refused to lie down.
Seven minutes after the restart Buffon did well to push Cesar's shot on to the post. At the other end, Pogba replied but skewed his shot wide while in space to the left of goal.
Juve came closest to levelling minutes later when Pereyra collected Dybala's threaded ball, powered into the area and unleashed a low drive only to see it come off the base of the upright.
Pogba missed making contact with the rebound and when it fell to Dybala, the Argentinian skied the follow-up, Juve holding their heads in frustration.
Cuadrado replaced Stefano Sturaro on 67 minutes, the Colombian's fresher legs and mazy runs giving Chievo an immediate challenge and Juve a sniff of a goal.
The on-loan Chelsea forward made an immediate impact, collecting Morata's flick-on to dribble his way into the box only to be shut out at the last second.
Cuadrado's most impressive feat, however, was winning a late penalty after what appeared to be the slightest of contact with the boot of Cesar deep in Chievo territory.
Dybala made no mistake, smashing the ball past the 'keeper and into the roof of the net to seal Juve's first points of the season.
Juventus sit in 16th place at six points behind Roma and Chievo, who regained top spot thanks to superior goals difference.
Earlier, Roma prepared for Wednesday's Group E clash against defending European champions Barcelona with a hard-fought 2-0 win away at Frosinone.
Iago Falque the opener for the Giallorossi, who rolled with the punches proffered by the league new boys before Juan Iturbe put the match beyond reach at the death with a fine individual strike.
Garcia paid tribute to Frosinone, and while hailing Roma's defence he regretted their lack of real chances on goal.
"Fair play to Frosinone, they battled throughout and if they keep that up they'll have a good season," Garcia told Sky Sport.
"I'm happy with the attitude we showed, although we didn't have enough shots on goal. There's still work to do but we defended well.
"We needed the three points and that's what we got."