The Partenopei held their nerve in a tough-looking fixture to climb a point in front of Juventus, who temporarily moved top with victory at Fiorentina on Friday night.
Dries Mertens rounded off the scoring with Napoli's fourth 17 minutes from time, helping to extend his side's winning league run to eight matches in the process.
The home side responded well, creating a couple of half-chances before Lorenzo Insigne curled the ball just wide of the target.
Marco Parolo then failed to keep his header down from a good position and Insigne was marginally off the mark with his intended lob.
Napoli did manage to drag themselves back on level terms with two minutes of the first half left to play, though, as Jose Callejon latched on to Jorginho's free kick and fired the ball into the back of the net.
The Brazilian defender was at fault for Napoli's key second goal, too, sliding in to convert Callejon's cross that was intended for Insigne at the back post.
Napoli's third followed two minutes later, this time through a deflected shot off Piotr Zielinski that left Strakosha wrong-footed in the visiting goal.
Strakosha was being kept busy for the remainder of the match, particularly when blocking Zielinski's attempt, but the league leaders showed why they are so highly fancied this term by adding a fourth before the end.
Mertens dinked the ball over Strakosha at the end of an impressive team move, taking the Partenopei another game closer to Serie A glory.
NAPOLI (4-3-3): Reina; Hysaj, Tonelli, Koulibaly, Mario Rui; Allan (Rog 81'), Jorginho, Hamsik (Zielinski 46'); Callejon (Maggio 84'), Mertens, Insigne
LAZIO (3-5-1-1): Strakosha; Wallace, De Vrij, Radu; Marusic, Milinkovic-Savic, Leiva (Nani 67'), Parolo, Lulic (Lukaku 60'); Luis Alberto (Caicedo 60'); Immobile