Following Juventus' 4-0 triumph over Cagliari earlier in the day, only three points would see Antonio Conte's charges reclaim top spot in Serie A.
The visitors got the start they wanted when Romelu Lukaku took advantage of a defensive error to race clear on goal and slot into the bottom corner after 14 minutes.
The lead was doubled 20 minutes later as Lukaku registered his second of the night with a powerful strike from around 20-yards out after collecting a neat pass from Marcelo Brozovic.
While it was a dominant first half for the visiting side, Napoli managed to pull a goal back five minutes before the halftime break through Arkadiusz Milik, who turned home a cross from Jose Callejon.
After a quiet start to the second half, Inter managed to restore their two-goal advantage just after the hour mark thanks to Lautaro Martinez's ninth league of the season.
Napoli continued to show fight despite conceding a third goal as Lorenzo Insigne rattled the crossbar with an impressive free-kick that left Samir Handanovic flat-footed.
In the end, Conte's troops were able to see out the rest of the clash with relative ease to victory and reclaim top spot.
AC Milan 0-0 Sampdoria
Atalanta 5-0 Parma
Bologna 1-1 Fiorentina
Lecce 0-1 Udinese