Following the rarest of home defeats for champions Juventus against Lazio earlier in the day, the Partenopei earned the three points through Insigne's landmark strike 20 minutes into the game in the Italian capital.
Napoli are now five points ahead of closest challengers Lazio, Juve and Inter Milan, with the latter due to play their game in hand against rivals AC Milan on Sunday evening.
The visitors, who have now won eight from eight in the Italian top flight, came close to taking the lead 18 minutes into the match when Insigne was played through on goal.
Alisson Becker produced a big stop to deny the Italy international on that occasion, but just moments later the ball was this time in the back of the net for what proved to be the winner.
A fortunate deflection saw the ball land nicely for Insigne to take on, tucking it past Alisson to bag the 200th goal of Maurizio Sarri's tenure.
All the late questions were being asked by the Giallorossi, without key man Kevin Strootman today, as Reina produced one big save and Dzeko skimmed the crossbar with his headed attempt.
There was to be one final chance for Cengiz Under right at the very death, but he volleyed straight at Reina when picked out in a good position unmarked inside the area.