Former Lazio star Stephan Lichtsteiner scored the winner as Juventus progressed to the Coppa Italia semi-finals with a 1-0 win at the Stadio Olimpico on Wednesday.
Lichtsteiner's second-half goal sealed an 11th-straight win in domestic competitions for the holders, who overcame Lazio in last season's Coppa final to seal a domestic double.
Juventus took the lead on 65 minutes when Zaza's shot came back off the post and Berisha thought he had saved Lichtsteiner's effort on the rebound, but the ball was just over the line. Inter await Juve in a blockbuster semi-final after they defeated Napoli on Tuesday.
Juve wing-back Lichtsteiner had the game's first effort on six minutes, but his long range strike was straight at Berisha.
The hosts should have been ahead after 12 minutes. Senad Lulic's pass freed Keita down the left but after advancing on goal he hit his shot well over the target from just eight yards.
Allegri's men then wasted a glorious chance to open the scoring on 51 minutes.
But Juve eventually did take the lead on 65 minutes. Zaza's curling effort beat Berisha but rebounded off the post to Lichtsteiner, whose low shot crept over the line despite the goalkeeper's efforts.
