Substitute Higuain slotted home on 80 minutes after fellow Argentine Paulo Dybala had opened the scoring in the fourth minute at the San Siro.
Another Argentine forward Lautaro Martinez pulled Inter Milan level from the spot on 18 minutes, but coach Antonio Conte lost in his first meeting against his former club since leaving Juve to take over the Italy national team in 2014.
Juventus moved one point ahead of Inter after seven games as they target a ninth consecutive title, and first under Maurizo Sarri.
“Overtaking at the top is insignificant right now,” said former Chelsea boss Sarri.
“The important things is that we showed a performance of character and personality against a strong team in a high-tension environment. We deserved to win.”
Sarri started with Dybala and Federico Bernardeschi up front alongside Cristiano Ronaldo.
Higuain — who also scored in Juventus’s 3-0 Champions League win over Bayer Leverkusen during the week — began on the bench.
The champions got off to a blistering start with Miralem Pjanic setting up Dybala who took Inter goalkeeper Samir Handanovic by surprise.
Ronaldo rattled the crossbar and then had a goal ruled out when Dybala was in an offside position.
But Inter got back on level terms when Juventus defender Matthijs de Ligt handled the ball, with Lautaro drilling past Wojciech Szczesny.
The hosts were hit with Stefano Sensi going off injured with Sarri making a double substitution after an hour bringing on in-form Higuain and Rodrigo Bentacur.
Ronaldo and Bentancur combined to send Higuain through for the winner, with Szczesny doing well to deny Matias Vecino as Inter desperately pushed forward for an equaliser.
“Juve showed their heavy artillery,” said Conte, who coached the Turin giants to the first three of their current run of eight consecutive titles.
“Congratulations to them, we’ll roll up our sleeves now,” added Conte whose side lost their midweek Champions League game to Barcelona 2-1.
– Napoli held –
Gian Piero Gasperini’s Atalanta celebrated moving back to the newly-named Gewiss Stadium with a 3-1 win over promoted Lecce that keeps the Bergamo side third on 16 points.
But Serie A runners-up Napoli are now six points behind Juventus in fourth following a goalless draw at Torino.
“We want to fight for the Scudetto, but our ranking makes us cry a little,” said Napoli coach Carlo Ancelotti.
Roma are fifth, a point behind Napoli, with their match against Cagliari at the Stadio Olimpico finishing 1-1 after Nikola Kalinic’s last-gasp goal for the hosts was disallowed.
“Sick and tired of this crap costing us games. Too many times already this year,” said Roma owner Jim Pallotta on Twitter.
Joao Pedro’s early penalty after a Gianluca Mancini handball was cancelled out by Luca Ceppitelli’s own goal before half-time.
But what looked like a winner from Kalinic was disallowed without a VAR review for a foul on Fabio Pisacane which saw the Cagliari defender stretchered off.
Roma were furious with coach Paulo Fonseca and his deputy both banished from the sideline before the final whistle.
Roma stay a point ahead of city rivals Lazio, who drew 2-2 at Bologna with Serie A top scorer Ciro Immobile getting both goals for the visitors, to bring his tally to seven goals in as many games.
Lazio’s Joaquin Correa missed a chance for the winner when he sent a penalty kick over the bar two minutes from time.
Bologna coach Sinisa Mihajlovic — a former Lazio player — was back on the bench after undergoing a second round of chemotherapy to treat his leukaemia.
Both teams finished with 10 men after Lazio’s Lucas Leiva was sent off on the hour mark with Bologna’s Gary Medel following nine minutes later.
In Tuscany, Nikola Milenkovic nodded in the only goal after 72 minutes to give Fiorentina their third consecutive win as Udinese fell to their fourth defeat in seven games.
Fiorentina are eighth with Udinese a point above the relegation zone.
