Carlo Ancelotti's hosts slipped off the pace last weekend with a loss to Juve in Turin, but managed to avoid dropping further adrift, after the embattled Cristiano Ronaldo scored in the reigning champions' victory at Udinese on Saturday.
"We played some really good football today, even if Sassuolo were not an easy opponent to deal with," said Ancelotti.
Algerian youngster Ounas, making his full debut in Serie A, gave Napoli the perfect start with a magnificent goal in only the third minute.
The 21-year-old latched onto a poor back-pass from Manuel Locatelli, flicked the ball over the head of visiting centre-back Giangiacomo Magnani, and hammered home a stunning left-footed volley to score his first goal in Italian football.
The home team dominated throughout, with Dries Mertens drilling an effort wide before sending an attempted lob from the halfway line floating over.
But Insigne came off the bench early in the second half and secured the win in trademark style with 18 minutes remaining, cutting inside off the left wing and curling a ferocious shot into the far top corner.
"I am going through a good period of form, I hope to continue like this and to keep scoring regularly, but aside from all that, I really hope Napoli can go all the way in every competition," said Insigne, who also scored the winner against Liverpool in the Champions League on Wednesday.
Napoli finished the game playing against 10 men, after Sassuolo wing-back Rogerio's late red card.