Inter Milan needed a stoppage time goal from debutant Stevan Jovetic to beat Atalanta 1-0.
Mihajlovic’s previous club Sampdoria gave Carpi a baptism of fire by smashing five goals past the Serie A newcomers in the first 37 minutes, although the visitors finished with a more respectable 5-2 scoreline.
Juve’s defeat ended their 47-match unbeaten home league record — a run stretching back to January 2013 — and ensured that the Turin side began their pursuit of a fifth straight title in miserable fashion.
Juve enjoyed the lion’s share of the chances but were unable to respond when French striker Cyril Thereau finished from close range after 78 minutes following an excellent cross from Panagiotis Kone.
“We are still under construction,” Juve coach Massimiliano Allegri, who has lost Carlos Tevez, Andrea Pirlo and Arturo Vidal from last season, told Sky Sports Italia. “We must have patience to rebuild.
“It’s to be expected when you have so many new players, it takes a while to refine the mechanism.”
At the Artemio Franchi, Fiorentina made sure Milan’s miserable form from last season continued.
Milan defender Rodrigo Ely was sent off after 37 minutes for a second bookable offence and Marcos Alonso sent the resulting free kick past Diego Lopez from 30 metres.
Fiore, now managed by former Basel coach Paulo Sousa, doubled their lead after 56 minutes when Josip Ilicic converted a penalty after Alessio Romagnoli brought down the Slovenia midfielder.
Napoli, where former Empoli coach Maurizio Sarri has replaced Rafael Benitez on the bench, took a third-minute lead
through Marek Hamsik but failed to capitalise on their good start.
Antonio Floro Flores levelled just after half an hour and Nicola Sansone grabbed the winner with six minutes left.
Roberto Mancini’s Inter struggled to break down stubborn Atalanta at San Siro until Jovetic curled in a delightful effort in the third minute of stoppage time.
Carpi’s dream turned into a nightmare as two goals each from Eder, including a penalty, and Luis Muriel and a Fernando free kick saw them five goals behind at Sampdoria, where Walter Zenga has replaced Mihajlovic as coach.
However, Andrea Lazzari pulled one back before the break and Ryder Matos scored with a curling effort in the 88th. Lazzari then saw a stoppage-time penalty saved by Emiliano Viviano.
Frosinone, who like Carpi were making their Serie A debut, went ahead with a Danilo Soddimo goal in the seventh minute against Torino before Fabio Quagliarella and Daniele Baselli turned the game around in the second half for the visitors who ran out 2-1 winners.
Chievo scored three times in nine minutes as they came from behind to win 3-1 at Empoli and Abdelhamid El Kaoutari scored in stoppage time to give Palermo a 1-0 win over Genoa.
(Editing by Mark Meadows and Ken Ferris)