Top-ranked Djokovic stretched his Grand Slam win streak to 26 matches by eliminating sixth seed Berrettini 5-7, 6-2, 6-2, 6-3 at Arthur Ashe Stadium in a rematch of July's Wimbledon final
World number one Djokovic rallied past 99th-ranked Brooksby 1-6, 6-3, 6-2, 6-2 to book a quarter-final encounter with Italian sixth seed Matteo Berrettini in a rematch of July's Wimbledon final
The 25-year-old Italian put his booming serve and crunching forehand to good use against the 64th-ranked Bedene whom he defeated in four sets on his way to the second week of the grasscourt Grand Slam in 2019.
Eighth seed Berrettini, who has dropped only one set in the tournament, will be aiming to win his maiden ATP Masters 1000 title against Zverev on Sunday.
The tournament is organised by the 33-year-old's family with his younger brother Djordje acting as director, and will be played in his "Novak" facility where he regularly trains.
Musetti, just turned 19, is the youngest player in the ATP top 100, with Berettini 24, Sonego 25, Mager 26, Caruso and Cecchinato, both 28, and Travaglia, 29.