Carlos Tevez was in sublime form as he scored a hat-trick and also set a goal up for Federico Peluso in the Turin giants' eighth successive league victory - a run in which they have not conceded a goal.
It was another statement of intent for Antonio Conte's side, who showed a positive response to being knocked out of the UEFA Champions League with a defeat at Galatasaray on Wednesday.
Napoli's Champions League campaign also ended in midweek and they took their frustration out on Inter in a thrilling clash at Stadio San Paolo.
Ricky Alvarez was sent off in the second half and Jose Callejon sealed the points before Inter goalkeeper Samir Handovic produced a fine reflex save to keep out Goran Pandev's penalty, as Napoli cut the gap to second-placed Roma to two points.
Josip Ilicic, Borja Valero and Giuseppe Rossi were on target as Vincenzo Montella's side got back on track following defeat at Roma last weekend.
Livorno were unable to climb out of the relegation zone as Lazio striker Miroslav Klose's first-half double consigned them to a 2-0 defeat in Rome.
