After a dominant opening set, World No. 325 Barty found herself broken three times and losing the second set to love. She turned it around in the final set to upset the No.89 Sakkari 6-4, 0-6, 6-3.
The two other seeds in action also eased into the second round, after No.6 seed Evgeniya Rodina cruised past local qualifier Pei-Chi Lee 6-2, 6-1 and No.8 seed Marina Erakovic overcame lucky loser Kyoka Okamura 6-4, 6-2.
Also in action, 2013 champion Alison Van Uytvanck had little trouble overcoming Japan's Hiroto Kuwata, advancing 6-0, 6-1 after just 55 minutes.
Ipek Soylu is also through to the second round after Daniela Hantuchova was forced to retire at 5-7, 6-2, 4-2 with an abdominal injury, and American Julia Boserup weathered a late challenge from Riko Sawayanagi to advance 6-2, 7-5.