Stephan Lichtsteiner scored Juve's winner early in the second half of a game in which both teams struggled on a difficult pitch that cut up badly following a hailstorm at half-time.
Inter's Colombian Fredy Guarin scored the first goal and set up a second for Diego Milito as they took a 2-0 halftime lead against Napoli, who had started the weekend in second.
Edinson Cavani pulled one back for the visitors early in the second half, the Uruguayan's 11th league goal of the season, and the rest of the match was an end-to-end affair in which almost every attack produced a chance.
Juve's victory, their 12th in 16 league games, took them on to 38 points, four ahead of Inter with Napoli a further point back in third place.
"The last four months have been painful," Juve coach Conte told reporters. "It's hard to be kept out of the 90 minutes after you have prepared the team with passion and enthusiasm."
Guarin, one of seven South Americans in Inter's starting lineup, opened the scoring in the eighth minute at freezing San Siro when he volleyed home Antonio Cassano's corner at the far post.
Cavani pulled one back for Napoli after an astonishing scramble in the 54th minute and they had numerous chances to equalise after that with Inter's Alvaro Pereira desperately lucky not to concede an own goal.
In Turin, Milan lost midfielder Nigel de Jong in the 21st minute and Torino went ahead seven minutes later when Antonio Nocerino's dreadful backpass was intercepted by Mario Santana, who ran into the box and rounded Marco Amelia to score.
Milan's Brazil forward Robinho levelled from a tight angle five minutes before hal
