- Arkadiusz Milik (57')
- Mohamed Kaba (90'+3')
The home fans collectively breathed a sigh of relief when Milik tapped the ball in from a short distance following Adrien Rabiot's header back across the face of the goal.
Juve moved up to 13 points, two behind Inter Milan, who host Sassuolo on Wednesday. Lecce are fourth on 11 points after suffering their first Serie A defeat of the season.
Lecce were solid in their defence but failed to register a single shot on target.
"We were up against a Lecce side that allowed you very little, but we stayed balanced and made the most of our chances," Juve manager Massimiliano Allegri told DAZN.
Juve supporters, who had hoped for redemption following Saturday's 4-2 loss at Sassuolo, were left frustrated after a dull first half ended without any goals.
"It was important to get the win, especially after a chaotic defeat against Sassuolo," Allegri added.
Federico Chiesa came closest to scoring for Juve in the first half, but his angled drive inside the box narrowly missed the target by inches.
Lecce went down to 10 men three minutes into stoppage time after Mohamed Kaba earning a second yellow card for diving.
Allegri played down his team's ambitions for this season.
"Over the last few days we have gone from Scudetto rivals for Inter to being flops, so there has to be a little balance in the way we are talked about," he said.
"We have many players without a great deal of experience, but they can grow. It takes patience and time to absorb errors and learn from them."
Juventus will visit Atalanta on Sunday.
- Antonio Giua