The Croat broke the deadlock in the 66th minute with his seventh league goal of the campaign after Juve survived a bout of first-half pressure which saw Roberto Gagliardini hit the post.
The win put Juve on 43 points out of a possible 45 at the top, 11 clear of second-placed Napoli who host Frosinone on Saturday, as they chase an eighth successive title.
Inter are third after their fourth defeat of the season and are now 14 points adrift of the Turin side.
"Mandzukic is a great forward," Juve coach Massimiliano Allegri said of his match-winner. "He's one of those players, who even on a bad day, can bring his physical presence to the game and make the difference.
Despite Juve's dominance in the standings, it was an even match and Inter, who have not won in Turin for six years, had two good chances in quick succession during the first-half.
A clever combination between Matteo Politano and Mauro Icardi produced a clear opening for Gagliardini but he did not connect cleanly and hit the inside of the post.
Then Perisic hooked wide after Politano did superbly to pull the ball back.