Substitute Giuseppe Rossi was on target for fourth-placed Fiorentina on his Serie A comeback after suffering a knee injury in January.
Napoli and Cagliari played a pedestrian opening half hour before Dries Mertens fired the hosts ahead with a 33rd minute penalty and Goran Pandev added another before halftime.
Marek Hamsik missed another penalty for Napoli in the 56th minute, after Cagliari goalkeeper Marco Silvestri had been sent off, but midfielder Blerim Dzemaili scored the third one minute later.
Rafael Benitez's Napoli, who won the Italian Cup on Saturday, have 72 points from 36 games and will go into the fourth qualifying round of next season's Champions League, the final round before the group stage.
Champions Juventus and second-placed AS Roma have already made sure of the automatic group stage places.
Fiorentina (61 points) have qualified for the Europa League leaving Inter Milan (57), Torino (55), AC Milan and Parma (54), Verona and Lazio (53) to battle for the two remaining places.
Berardi, 19, opened his account with a 23rd minute penalty, finished off a counter-attack nine minutes later and scored again from a narrow angle three minutes before the break, taking his tally for his debut top-flight season to 16.
Gonzalo Rodriguez pulled one back just before the hour only for Nicola Sansone to make it 4-1 seven minutes later.
Rossi came on in the 65th minute and needed just seven minutes to make his mark, scoring after a one-two with Borja Valero. Juan Cuadrado pulled another back two minutes later.
Rossi made his comeback this season after being sidelined for nearly two years with a knee injury and scored 14 goals before suffering another, less serious injury, in January.
Sassulo, 16th in the 20-team table, have 31 points followed by Chievo (30), Bologna (29), Catania (26) and Livorno (25).
(Reporting By Brian Homewood, editing by Pritha Sarkar)
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