Ex-Milan coach Allegri will be delighted with the display of 18-year-old French striker Kingsley Coman, a close-season free transfer signing from Paris Saint Germain.
Coman, paired with a slimmed-down Carlos Tevez in attack, looked confident, sharp and dangerous throughout his Serie A debut.
The decisive goal came when Juve’s Uruguayan defender Martin Caceres got on the end of a corner at the back post and saw his powerful header was turned in by Biraghi, who is on loan at Chievo from Inter Milan.
Coman went close with a fierce shot on the turn in the 36th minute that force a fine save out of Chievo keeper Francesco Bardi, also on loan from Inter.
The woodwork kept Chievo in the game though – Tevez and Caceres both hitting the bar shortly before the break as Juventus looked to extend their lead.
After the interval, Juve, without injured playmaker Andrea Pirlo, continued to press forward and enjoy the better of the possession although their keeper Gianluigi Buffon had to be sharp to foil a Maxi Lopez drive in the 77th minute.
Allegri said he was pleased with the first outing of his team, who have won the last three Serie A titles.
“I was a little worried at the end because after all those chances we missed, we risked it and needed Buffon to make a great save,” said the Juventus coach.
“We had enough chances to close out the game, We were a bit too worn out at the end but it was a good game and now we can get some players back during the (international) break,” added Allegri.
Roma are viewed by many as the team most likely to challenge Juve at the top this year and they made a positive start to their campaign with Ivory Coast forward Gervinho creating one goal and grabbing the second against Fiorentina.
Former Chelsea and England fullback Ashley Cole made his Serie A debut against a Fiore team coached by ex-Roma striker Vincenzo Montella.
Belgian midfielder Raddja Nainggolan opened the scoring in the 28th minute, bursting through from midfield and feeding Gervinho, whose low shot was parried by Fiorentina’s Brazilian keeper Neto only for Nainggolan to blast home the loose ball.
Fiore twice went close to an equaliser just after the hour – Josip Ilicic hitting the bar with a curling free-kick before Khouma Babacar’s close-range effort was well blocked by Roma keeper Morgan De Sanctis.
But in injury time Roma wrapped up the three points with Nainggolan returning the favour to Gervinho with a perfectly weighted through ball and the Ivorian rounding Neto before slotting into the unguarded goal.
The first Sunday of the season sees Filippo Inzaghi’s AC Milan host Lazio while Inter are at Torino and Napoli travel to Genoa.
(Reporting by Simon Evans, editing by Pritha Sarkar and Ken Ferris)