Fiorentina moved above Napoli in Serie A and consigned coach Gennaro Gattuso to a fourth defeat in five games with a 2-0 victory at Stadio San Paolo on Saturday.
Fiorentina coach Giuseppe Iachini is unbeaten since taking over in December. He earned a draw at Bologna on his debut before leading his side to three wins in the space of a week by beating SPAL in the league and knocking Atalanta out of the Coppa Italia before the victory in Naples.
"As soon as Iachini arrived, we talked and immediately understood what we wanted to do," goalscorer Chiesa told DAZN.
"Fiorentina were not in a good situation before the winter break, so we needed to turn things around and we're all very united now."
The result lifts Fiorentina up to 12th place on 24 points, level with Napoli but above them on head-to-head record, while continuing Gattuso's wretched start since replacing Carlo Ancelotti as coach last month.
The home crowd loudly booed their team off at fulltime as Napoli fell to a third consecutive league defeat for the first time since April 2012.
Fiorentina went in front after 26 minutes when Chiesa finished off a well-worked team move by stabbing home a finish from 12 yards.
The visitors came close to doubling their advantage just five minutes later when David Ospina clawed a Gaetano Castrovilli header from under the bar, before Patrick Cutrone hammered a shot past the goalkeeper only to ruled offside.
Napoli mustered a response with good chances either side of halftime, as Jose Callejon sent a free header wide from inside the area before Lorenzo Insigne's long-range effort clipped the outside of the post.
But substitute Vlahovic provided the killer blow on the 74th minute, cutting inside the box to curl a superb left-footed finish into the far corner beyond the diving Ospina.