Argentina international Higuain, signed from Napoli for €88m in July, fired home from close range in the second half after Fiorentina striker Nikola Kalinic had cancelled out Sami Khedira’s brilliant first-half header.
Juve secured a fifth straight Scudetto last season and appeared to be cruising in the first period, but they only had Khedira’s goal to show for their dominance and nearly paid the price for wayward finishing when Kalinic stole in for a shock 70th-minute equaliser.
But Higuain, who equalled an 87-year-old Serie A record when scoring 36 league goals for Napoli last season, popped up when it mattered to spare Juve’s blushes, ensuring they made a winning start.
Roma launched their league campaign in style at the Stadio Olimpico thanks to two second-half Diego Perotti penalties and strikes from Edin Dzeko and Mohamed Salah in a 4-0 win against Udinese.
Argentinian midfielder Perotti, a 56th-minute substitute for Stephan El Shaarawy, converted two spot-kicks in the space of 10 second-half minutes before striker Dzeko added a third in the 82nd minute, with Salah completing the scoring with his first league goal two minutes later.
In Spain, Gareth Bale opened and closed a convincing Real Madrid win at Real Sociedad, heading home in the second minute and running in the third in injury time.
Marco Asensio scored the second for a Madrid side without Ronaldo following his Euro 2016 knee injury.
Luis Suarez scored a hat-trick on the opening day of La Liga as champions Barcelona thrashed Real Betis 6-2. Arda Turan opened the scoring for Barca from close range, before Ruben Castro levelled from a free-kick.
Lionel Messi slammed home an excellent 22-yard strike before Suarez swept home from the edge of the box.
Suarez scored the fourth, Messi drove home from distance and Suarez curled home a free-kick for his third, before Castro added a late consolation.
Uruguay striker Suarez, last season’s La Liga top scorer with 40 goals, has now scored 17 goals in his past six league games.
It was Barcelona’s third game of the season, having beaten Sevilla 2-0 and 3-0 in the two legs of the Spanish Super Cup.
After the match, Barca confirmed “the beginning of an agreement with Manchester City for Claudio Bravo”, the 33-year-old keeper who played against Gus Poyet’s Betis.
Sevilla began their La Liga campaign with a thrilling 6-4 victory over Espanyol on Saturday evening.