Chievo 0 Juventus 1: Allegri enjoys winning start
New coach Massimiliano Allegri saw his side deliver an ominous display that should have resulted in a wider margin of victory.
Biraghi deflected a header from Martin Caceres into his own net after seven minutes, but Juve were unlucky not to find the net again as Arturo Vidal struck a post and Carlos Tevez twice hit the crossbar.
Chile midfielder Vidal also saw an effort cleared off the line, although Chievo spurned a late chance to equalise when Maxi Lopez was denied by Gianluigi Buffon.
The intensity of Juventus' performance dipped in the second period, but Kingsley Coman twice went close on an encouraging debut.
Allegri was without the injured Andrea Pirlo, but his team almost got off to a dream start as Tevez dragged an effort wide in the first minute.
The reigning champions were quickly into their stride and took the lead when Tevez's deep corner was met by Caceres, who nodded home at the back post with the aid of a deflection off Biraghi.
Chievo, winless against Juventus since 2010, almost found a response when Lopez - making his debut - controlled in the area and turned before missing the target.
Key midfielder Vidal, the subject of much transfer speculation this summer, was a constant menace and twice went close to extending Juve's lead.
After his initial shot had been blocked on the line, Vidal saw a diving header cannon off the post and Juve hit the woodwork on two further occasions before the break.
Tevez's half-volley from Stephan Lichtsteiner's dangerous centre hit the crossbar and the Argentinian also struck the bar with a looping header.
The impressive Coman almost marked his bow with a fine goal early in the second half, curling an effort narrowly wide.
A beautiful cross from Vidal was headed over by the teenage Frenchman, with Juve continuing to appear in control.
Yet for all Juve's dominance, Lopez missed a golden chance for the hosts late on, Buffon making a sprawling save after the ball had fell kindly for Chievo's Argentine forward 12 yards out.
There were no further scares for the visitors, who handed a first appearance to Roberto Pereyra as a replacement for Vidal.
Chievo saw coach Eugenio Corini dismissed in stoppage time after he appeared to take a step onto the field to retrieve the ball for a throw-in.