Luciano Spalletti's third-placed Inter fall 14 points adrift of the leaders with the Derby d'Italia defeat a grave blow to their hopes of challenging for a first title since 2010.
Unbeaten Juventus have 43 points from 15 games -- 11 points ahead of second-placed Napoli who host lowly Frosinone on Sunday -- with their only points dropped coming in a home draw against Genoa.
World Cup runner-up Mandzukic's diving header after 66 minutes off a cross from former Inter player Joao Cancelo was enough to decide the outcome at the Allianz Stadium.
"Mandzukic is one of those players who even on an off day can bring his physicality to the game and that can make the difference," said Juventus coach Massimiliano Allegri.
"We knew the championship wouldn't end today, but we still absolutely had to avoid defeat.
"I asked the lads to be efficient and effective. We were only half that in the first period, but then we started to hold the ball with greater patience, were more organised and solid.
"After that, the quality of the players inevitably emerges."
'Juve smart, Inter naive'
The seven-time reigning champions proved yet again they were a class above their rivals even with Portuguese star Cristiano Ronaldo not as omnipresent as he has been in previous games, failing to add to his ten league goals.
Inter captain Mauro Icardi also failed to muster a single shot on goal, but the visitors did have chances in the first half with Roberto Gagliardini rattling the post just before the half-hour mark.
"We played well enough but we weren't consistent, there were situations where we didn't interpret or read them property while Juventus did not do anything wrong," said Spalletti.
"If someone takes the lead, of course it makes the difference, but we made too many banal and cheap errors," continued the Inter coach.
"Unfortunately, Juve are smart and we are naive. They have a way of wasting five minutes after a foul."
Argentine Paulo Dybala threatened early for Juventus, nodding over a Ronaldo cross with Inter goalkeeper Samir Handanovic tipping over in the first ten minutes.
Icardi and Matteo Politano set up Gagliardini but his shot bounced off the post just before the half-hour mark.
Mandzukic got his head to Rodrigo Bentancur's cross although failed to control the finish with Marcelo Brozovic deflecting wide and Handanovic getting his hand to a searing Giorgio Chiellini header before the break.
Inter winger Politano missed a chance to break the deadlock just after the break as Leonardo Bonucci produced a vital block.
A Ronaldo strike from distance flew narrowly over the crossbar just before the hour mark, before Mandzukic's stooping header gave him his seventh goal this season.
Inter desperately tried to salvage a point but were closed down by a Juventus defence well-organised by veteran Chiellini, with Lautaro Martinez volleying wide in a last desperate attempt for the visitors.
Inter stay four points ahead of AC Milan, who host Torino, with Lazio a further point back in fifth before their game against Sampdoria.
Spalletti's side now turn to their crucial Champions League game against PSV Eindhoven at the San Siro on Tuesday.
Juventus are already through to the Champions League knock-out rounds before next week's trip to Young Boys in Switzerland.