The host raced into a five-goal lead within 37 minutes, with Eder and Luis Muriel both scoring twice, though Carpi did pull one back before half-time.
Sampdoria was reduced to 10 men when midfielder David Ivan received a second yellow, before Ryder Matos snatched a second for Carpi late on.
Juventus's defence of its Serie A title got off to a losing start as Cyril Thereau fired Udinese to a 1-0 victory in Turin.
The champion, in the hunt for a fifth successive Scudetto, were wasteful in front of goal and fell behind with 12 minutes remaining when Thereau tucked away Panagiotis Kone's cross.
Paulo Dybala came on to make his Serie A debut for his new club in the closing stages, but Udinese held firm to end Juve's 47-game unbeaten home streak in the league.
Former Sampdoria manager Sinisa Mihajlovic's start to life at the helm of AC Milan ended in defeat at the hands of Fiorentina, as goals either side of half-time from Marcos Alonso and Josip Ilicic sealed a 2-0 win for Paulo Sousa's side.
Milan was sluggish throughout and never looked likely to pose a threat to its host after Rodrigo Ely – making his Serie A debut – was sent off midway through the first half.
Nicola Sansone came off the bench to grab a late winner as Sassuolo came from behind to beat Napoli 2-1 at home, while Manchester City loanee Stevan Jovetic marked his return to Italy with a 94th-minute strike to give Inter a 1-0 victory over 10-man Atalanta.
Chievo was in terrific form away from home as it overcame Empoli 3-1, with Serie A newcomer Frosinone losing out 2-1 to Torino.
Meanwhile, Abdelhamid El Kaoutari's injury-time strike earned Palermo a 1-0 triumph over Genoa.