Captain Insigne scored four minutes from time after Domenico Berardi had put midtable Sassuolo into a 52nd minute lead in Modena.
Napoli's hopes of a first league title since 1990 have faded as Juventus continued their charge towards an eighth consecutive Scudetto with a 4-1 win over Udinese on Friday.
Napoli are far behind in second, six points ahead of AC Milan, who beat bottom club Chievo 2-1 on Saturday for a fifth league win in a row.
Inter Milan are a further point adrift in fourth.
"We did well to react and get a draw out of it, then tried to push for the victory," said Insigne.
"Now let's think about Salzburg," he added of their Europa League tie during the week where they can advance to the quarter-finals.
Inter meanwhile shook off pre-derby tensions with Matteo Politano and Roberto Gagliardini scoring in the second half to beat SPAL 2-0 to revive their Champions League chase.
Luciano Spalletti'a side had taken just a point from their last two games, and desperately needed a morale-boosting win to keep pace with AC Milan before next week's Derby della Madonnina.
Argentina star Mauro Icardi was not present in the San Siro, remaining sidelined since being stripped of the captaincy a month ago amid a contract dispute.
The 26-year-old also remains uncertain for Thursday's Europa League game against Eintracht Frankfurt and Sunday's derby, both at the San Siro.
"We should have done better at the start of the game, but we allowed the tension to choke us, and then became timid and insecure, but we're Inter and we had to win this game," said Spalletti.
"We have this fire within us, but every now and then it becomes a flicker.
"Once the goal went in, everyone was totally transformed and brimming with confidence."
Spalletti's side had been frustrated in the first half by SPAL who are just two points above the relegation zone.
Lautaro Martinez looked to have given Inter the lead after half an hour on front of 61,000 fans in the San Siro but a VAR review awarded handball.
The hosts also lost Croatian midfielder Marcelo Brozovic, who limped off, with Joao Miranda also exiting at the break with a suspected broken nose.
Politano finally broke through after 68 minutes with Gagliardini turning in a Cedric assist nine minutes later.
The race for Champions League football remains tight with Roma, Torino and Atalanta six points behind fourth-placed Inter Milan.
Lazio, with a game in hand, are two points off the Europa league places after a 1-1 draw at Fiorentina, with Ciro Immobile's 23rd minute goal cancelled out by Luis Muriel (61) for the hosts who are 10th.
Belotti lifts Torino
Torino continued their impressive form with Andrea Belotti claiming a double to extend their winning run to three games with a 2-1 win at Frosinone.
Walter Mazzarri's side move sixth and into the Europa League places, level on 44 points with Roma, who play at Empoli on Monday under new coach Claudio Ranieri, and Atalanta who beat Sampdoria 2-1.
Colombian Duvan Zapata broke through for the Bergamo outfit on 50 minutes and Robin Gosens scored the winner after 77 minutes.
Fabio Quagliarella had equalised for Sampdoria from the spot on 67 minutes as the 36-year-old went top of the Serie A goal-scoring charts with 20 in 27 games, one more than Juve star Cristiano Ronaldo.
Bologna earned a valuable three points with a 2-0 win over relegation rivals Cagliari.
Erick Pulgar and Roberto Soriano netted to give Bologna just their fourth win of the season as they remain third from bottom with Cagliari just six points clear of safety.