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.
"We were only efficient for half of the first period, but then we started to keep the ball with more patience and we were more organised and solid. After that, the quality of the players inevitably comes through."
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.
Juve threatened mainly from corners and defender Giorgio Chiellini had a near-post header tipped over by Samir Handanovic.
Inter wasted another opening early in the second half after Juve's Blaise Matuidi gave away possession but Politano passed the ball to Icardi who played it back and the home defence recovered as the pair dallied.
Inter paid the inevitable price midway through the second half when Matuidi's cross-field ball released Joao Cancelo on the left, the Portuguese crossed to the far post and Mandzukic got in front of Kwadwo Asamoah to head in.
Inter penned Juventus back for the last few minutes and substitute Lautaro Martinez volleyed wide from a poor Cancelo clearance in stoppage time but they could not find an equaliser.
"Taking the lead would have made a difference but we made too many basic errors," said Inter coach Luciano Spalletti. "Juve are cunning and we are naive.....they have a way of wasting five minutes after a foul."
"We played some very good football but there were some situations where we didn't read the game correctly." (Reporting by Brian Homewood; Editing by Ken Ferris)
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