Juventus were 4-0 up by half-time after Alex Sandro opened the scoring on nine minutes in Turin with a quick-fire Khedira brace and a Miralem Pjanic goal burying an overwhelmed Sassuolo who are rooted in 15th position.
Costa strike pushes Juventus closer to Napoli
Argentine ace Higuain dominated the second half with a hat-trick in a 20-minute spell to bring his league tally to 13.
But Napoli replied with goals in either half from Dries Mertens and Marek Hamsik keeping Maurizio Sarri's side one point ahead of the six-time defending champions.
"We cannot afford any slip-ups with Napoli having an extraordinary championship. It was important to win today so we could definitively break away from the chasing pack," said Juventus coach Massimiliano Allegri. "Many players are beginning to reach their peak."
Bernardeschi strike keeps Juventus on Napoli’s trail
The only bad news for Juventus was Blaise Matuidi picking up a muscular injury which Allegri said should keep the French international out of the Champions League clash against Tottenham on February 13.
In Naples, Mertens opened the scoring after 20 minutes at neighbouring Benevento with a magnificent lob from a tight angle, but the Belgian limped off with an ankle injury in the final minutes of the game.
Slovak Hamsik doubled their lead just after the break, meeting Jose Callejon's low cross for his 118th goal for the club.
Benevento had a few chances and were even awarded a penalty for a Kalidou Koulibaly tackle, only for it to be revoked by the video assistant referee (VAR) because of an earlier offside.
"We suffered at the start, but then broke the deadlock with a great goal from Dries Mertens," said Napoli skipper Hamsik. "Once we went 2-0 up, we tried to slow it down a bit and control the game. "We're not afraid of anyone, as we must only focus on our own results."
Earlier Roma got back to winning ways to move closer to the Champions League places with Turkish winger Cengiz Under scoring the only goal within the first minute in Verona.
Roma had not won since December 16 but 20-year-old Under got them off the mark early on taking the hosts by surprise to slot in his first Serie A goal.
The visitors held on despite Lorenzo Pellegrini being sent off after 51 minutes for tackling Ryder Matos from behind.
Roma stay fifth but move to within a point of Inter Milan who occupy the final Champions League spot after being held 1-1 by Crotone on Saturday.
Lazio in third — 14 points behind Napoli — host Genoa on Monday.
"We deservedly won. We went down to 10 men and still didn't allow a shot on goal," said Roma coach Eusebio Di Francesco.
Verona's Brazilian goalkeeper Nicolas did well to twice block Edin Dzeko, with Radja Nainggolan and Kevin Strootman also coming close before Roma held on for three points.
AC Milan missed the chance to move into the Europa League places, being held 1-1 at Udinese with Davide Calabria sent off on 68 minutes.
Suso put the visitors ahead with a stunning shot from distance in the ninth minute. But Milan's Calabria was sent off for a second yellow card midway through the second half and Udinese drew level eight minutes later when goalkeeper Gianluigi Donnarumma deflected into his own net.
Atalanta beat Chievo 1-0 with Gianluca Mancini's winner on 72 minutes at first disallowed, then given after viewing VAR.
Midtable Fiorentina won 2-1 at Bologna with Federico Chiesa getting the winner after 71 minutes after Jordan Veretout's opener was cancelled out by Erick Pulgar.
Cagliari earned a 2-0 win over relegation rivals SPAL in Sardinia, with goals from Luca Cigarini and substitute Marco Sau.
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