New Inter Milan boss Gian Piero Gasperini watched his side lose 4-3 at Palermo where he started Wesley Sneijder on the bench and saw his new three-man defence badly struggle.
Diego Milito twice gave the visitors the lead, flicking in Dejan Stankovic's errant shot and scoring a penalty but Palermo strike duo Fabrizio Miccoli and Abel Hernandez hit back.
Miccoli's superb late free-kick and Mauricio Pinilla's outrageous strike sealed the win for the Sicilians before an otherwise anonymous Diego Forlan marked his Inter debut with a stoppage-time goal for last term's runners-up.
Swiss right-back Stephan Lichtsteiner got the party started at Juve's 41,000-seat arena, which still does not have an official name after a failure to find a sponsor, when he converted fellow new signing Andrea Pirlo's great dinked pass.
"I need to thank all our fans, they kept us going for the whole game and gave the lads a real push. It's been the start that we were waiting for," new boss Conte, who won the 1996 European Cup with Juve as a midfielder, told reporters.
Sunday's performance bodes well with Parma's Sebastian Giovinco, co-owned by the hosts, only scoring from the spot late on after Juve's Paolo De Ceglie was dismissed for a professional foul.
Serie A's first round of matches last weekend was postponed because of a player strike over contracts but the season got underway on Friday when champions AC Milan drew 2-2 at home to Lazio. Napoli won 3-1 at Cesena on Saturday.
"How much time do I need? I don't know but I am staying 100 percent optimistic because i have a very good squad and I'm sure things will change," the Spaniard said.
Moestafa El Kabir added the Sardinians' second in injury time before Daniele De Rossi's consolation.
