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The Senegal striker fired in either half at Stadio Olimpico Grande Torino to send Napoli 21 points clear at the top, although second-placed Inter host Juventus later on Monday (AEDT).
After Osimhen opened the scoring in the early exchanges, the Partenopei soon had control as Khvicha Kvaratskhelia scored from the penalty spot.
Any hope of a Torino comeback was wiped away soon after the interval, Osimhen netting again before Tanguy Ndombele added another to keep Napoli on course for the crown.
It took just nine minutes for Napoli to take the lead, Osimhen meeting Piotr Zielinski's corner and heading a controlled finish into the far corner of Vanja Milinkovic-Savic's net.
The host would not be silenced though, Alex Meret denying a fierce Samuele Ricci drive before Nikola Vlasic poked the rebound onto the post from close range.
Napoli doubled its lead 10 minutes before the break as Kvaratskhelia slotted a penalty straight down the middle after being felled by Karol Linetty.
Osimhen struck a drilled effort from outside the box that required a diving save from Milinkovic-Savic, with Luciano Spalletti's visitors threatening to run rampant before the break.
Napoli struck again after 51 minutes as Kvaratskhelia's inventive flick found Mathias Olivera, who lofted an inviting left-wing cross for Osimhen to tuck home.
Kvaratskhelia capped a fine individual display in the 68th minute, unselfishly teeing up substitute Ndombele to poke under Milinkovic-Savic and wrap up a commanding win.
