The Croat netted what proved to be the winner in the 66th minute with his seventh league goal of the season after Juve survived a bout of first-half pressure which saw Roberto Gagliardini hit the post.
The Old Lady’s win puts them 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, who have not won at Juventus for six years, remain third but are now 14 points behind the Turin side.
Luciano Spaletti’s men were eventually punished for missing a host of chances at the Juventus Stadium.
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.
Later, Ivan 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 tippped 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.
The visitors paid the inevitable price midway through the second half when Matiudi’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.
In search of an equaliser, Inter penned Juventus back for the last few minutes and substitute Lautaro Martinez volleyed wide from a poor Cancelo clearance in stoppage time.