Mandzukic netted in the 44th minute by heading home his first goal since the New Year following Paul Pogba's delightful chipped pass.
Juve have 73 points from 31 matches, and while second-placed Napoli could cut their lead to three points with a win at relegation-threatened Udinese on Sunday, Massimiliano Allegri's side remain on course for a record fifth consecutive 'Scudetto'.
"It's an important victory for us. We need to keep racking up the points because Napoli aren’t giving in," said Allegri.
"Credit to the boys for winning 20 out of 21. Picking up victories is never easy at this stage."
Empoli, who had not won in 11 games before Saturday's match, should have taken the lead in the 14th minute but Riccardo Saponara blazed his shot over the bar from close range.
Mandzukic forced a smart save from Lukasz Skorupski soon after, before the impressive Alvaro Morata rattled the crossbar with a curling effort from outside the area in the 22nd minute.
Juve were frustrated in their attempts to extend their lead, with Skorupski saving from substitutes Kwadwo Asamoah and Simone Zaza in stoppage time, although Mandzukic's hallmark header proved enough to ensure a 20th victory in 21 Serie A games.
"It was important tonight that we got some players back from injury and earned three precious points," said Juve midfielder Claudio Marchisio.
"This is the final push, there are no more breaks or distractions. We just need to power through for the 'Scudetto'."
Empoli are 11th with 36 points after 31 matches.
Seventh-place Sassuolo won 3-1 at struggling Carpi in Saturday's early kick off to move onto 48 points.
On Sunday, Lazio face Roma while Torino travel to Inter Milan.
(Reporting by Ed Dove, editing by Pritha Sarkar)
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