Earlier, Kostyuk battled from a set down and overcame three rain interruptions to beat eighth seed Sakkari 0-6 7-5 6-2.
She became only the third women's player to beat a top-10 seed at Wimbledon in the Open Era after losing the first set 6-0.
American world number 10 Frances Tiafoe saw off China's Wimbledon debutant Wu Yibing 7-6(4) 6-3 6-4 before compatriot Taylor Fritz completed a 6-4 2-6 4-6 7-5 6-3 victory over Yannick Hanfmann.
Sixth seed Holger Rune sailed through to the second round for the first time with a 7-6(4) 6-3 6-2 victory over British wildcard George Loffhagen.
Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond and Toby DavisOur Standards: The Thomson Reuters Trust Principles.
Persons:
Serbia's Novak, Australia's Jordan Thompson, Dylan Martinez, Medvedev, Fritz, Novak Djokovic, Iga Swiatek, Spain's Sara Sorribes Tormo, Daria Kasatkina, Jodie Burrage, Daniil Medvedev, Arthur Fery, Marta Kostyuk, Maria Sakkari, Stefanos Tsitsipas, Dominic Thiem, Bulgarian Grigor Dimitrov, Japan's Sho Shimabukuro, Katie Boulter, Australian Daria Saville, Dimitrov, Briton Fery, Arthur, Kostyuk, Frances Tiafoe, Wu Yibing, Taylor Fritz, Yannick Hanfmann, Holger Rune, George Loffhagen, Shrivathsa Sridhar, Ed Osmond, Toby Davis
Organizations:
Lawn Tennis, Croquet Club, Wimbledon, All England Club, Stop Oil, Bulgarian, Security, Briton, British, Thomson
Locations:
London, Britain, Australian, Belarusian, British, Bengaluru