Full back Stephan Lichtsteiner, who spent three seasons at Lazio before joining Juventus, scored the only goal in the 66th minute as his side continued their excellent recent form.
After a slow start to the season, Juventus have won their last 10 Serie A games to put them second in the table and back in the hunt for a fifth successive league title. They have also reached the last 16 of the Champions League.
Juve, who thumped neighbours Torino 4-0 in the previous round, will face old rivals Inter Milan in a two-leg semi-final.
Lichtsteiner snapped up a rebound and the ball crossed the line before Lazio goalkeeper Etrit Berisha could clear it, after Simone Zaza's shot had hit the post.
Zaza was fielded alongside Alvaro Morata in a second-choice front line as coach Massimiliano Allegri rested Paulo Dybala and Mario Mandzukic.
"I don't like to use the word rotation because we have a competitive squad of an excellent standard," Allegri told reporters.
"Today, I would like to compliment (midfielder) Stefano Sturaro, Zaza and Morata, who has improved a great deal, and (Martin) Caceres, who contained (Lazio forward) Keita Balde, they all played a good match. It's difficult to leave anyone out."
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
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