Serbia’s Djokovic, 3 1, needed just one hour and eight minutes to acquire 6-3 6-0 against American Taylor Fritz.
Norrie lost 6-2 7-5 to Italian Lorenzo Sonego, ranked 40 places below him.
The British , who is set next week to rise into the top 50, fought to examine Sonego’s function and then was divided four times.
Norrie did break back when Sonego served for the match just to lose his function while the Italian went on to secure victory.
Best seed Djokovic converted half of 10 break points against Fritz since he moved closer to matching the listing of 33 Pros names of Rafael Nadal.
The reigning Wimbledon, US Open and Australian Open champion will face a last-eight meeting with Russian 10th seed Daniil Medvedev – who he overcome on his way to victory at Melbourne in January and have never dropped from three encounters.
Medvedev, 2-3, continued his good form against Greece’s Stefanos Tsitsipas, winning 6-2 1-6 6-4 to extend to four strikes his 100% record over the ATP second Gen champion – who climbed faulted on match point.