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Karolina Muchova overwhelmed Sorana Cirstea and will meet American Coco Gauff in the semifinals.
Djokovic improved his record against American opposition at the US Open to a perfect 12-0.
Sabalenka faces China's Zheng, who knocked out 2022 finalist Ons Jabeur, in the qusarterfinals.
It marked the 38th time Djokovic has won a five-setter and kept alive the 36-year-old's quest for a fourth US Open crown that would pull him level with Margaret Court's record haul of 24 Grand Slams.
The British charge at the US Open will carry on without 2012 champion Andy Murray, who was outclassed by Bulgarian Grigor Dimitrov.
The win was Djokovic's 95th career title and 39th Masters 1000 crown.
Djokovic recently had a five-set Wimbledon final which he narrowly lost to Spain's world number one, Carlos Alcaraz.
The Spaniard defeated the veteran in a thrilling five-setter.
Djokovic, who overwhelmed Alcaraz in the French Open semifinals last month, is bidding for a record-equalling eighth Wimbledon crown to become the oldest men's champion and match Margaret Court's all-time record of 24 Grand Slams.
The Serb won the quarterfinals, 4-6 6-1 6-4 6-3, to stay on track for his fifth straight title.