Serbian Djokovic, a four-time champion in Shanghai, steamrolled his 30th-ranked Italian Cobolli to post a 6-1, 6-2 in just over an hour.
The match initially scheduled for Tuesday at Wimbledon’s Plough Lane had to be postponed due to pitch damage following extensive flooding in South London.
Fritz was bundled out 6-4, 3-6, 6-3 by France's Arthur Fils, shortly after compatriot Tiafoe was eliminated with a 7-5, 6-3 loss to fellow American Brandon Nakashima.
Benfica's Kerem Akturkoglu, Angel Di Maria, Alexander Bah and Orkun Kokcu scored in a 4-0 demolition of Atletico Madrid in the Champions League.
Donovan Mitchell scored a season-high 36 points against Chicago Bulls as the Cleveland Cavaliers became just the eighth NBA team to begin a season with 12 straight wins.