Napoli took the lead with one of their trademark team moves. Dries Mertens found Marek Hamsik with a through ball and he crossed for Jose Callejon to tap in at the far post.
Insigne should have doubled Napoli’s lead on the stroke of halftime but he curled his shot wide with only the goalkeeper to beat.
However, the Italy international did score six minutes in to the second half, finishing off Allan’s chipped pass from outside the area.
Inisgne finished off the match in style for Napoli with a goal in stoppage time.
Napoli remain four points behind second-place Roma, with seven rounds remaining, and are seven clear of fourth-place Lazio.
Edin Dzeko continued his battle to finish the season as the league’s top goalscorer with the third goal in Roma’s 3-0 win over Bologna.
It was Dzeko’s 24th Serie A goal this campaign and sees him remain joint top with Torino forward Andrea Belotti, who also scored on Sunday.
It was an easy finish for Dzeko after Diego Perotti drew out Bologna goalkeeper Antonio Mirante before rolling the ball across for the Bosnia and Herzegovina forward to deposit into an empty net.
Federico Fazio and Mohamed Salah were on target in the first half as second-place Roma cut the gap back to six points on leader Juventus.
Inter Milan’s hopes of qualifying for Europe were dented by a shock 2-1 defeat at relegation-threatened Crotone.
Crotone took a deserved lead in the 18th minute when Gary Medel handled in the area and Diego Falcinelli drilled the resulting penalty into the bottom left corner.
Falcinelli doubled his tally four minutes later as he narrowly avoided being caught offside, sprinted forward and lifted the ball over Samir Handanovic.
Inter replied in the 65th when Ever Banega’s corner was nodded on by Geoffrey Kondogbia for Danilo D’Ambrosio to volley in from close range.
Inter dropped to seventh, two points behind AC Milan, who recorded a comfortable 4-0 victory over Palermo.
Suso came back from injury and scored an early free kick, before setting up Mario Pasalic for Milan’s second.
Carlos Bacca headed in a third before half-time and Gerard Deulofeu scored after the break.
Palermo defender Giancarlo Gonzalez was sent off after a second booking seven minutes from time.
Elsewhere, Torino came from behind to win 3-2 at Cagliari. Han Kwang-song had become the first North Korean to play in Serie A when he came on for the final four minutes against Palermo last weekend and the 18-year-old netted Cagliari’s second in stoppage time.