Zhang Shuai, a two-time WTA Guangzhou Open champion, was upset on Thursday, but Sofia Kenin recovered to advance and Sam Stosur also won.
The two-time champion, whose only WTA Tour singles titles have come at this event, came up short as Golubic ran out a 6-3 3-6 6-4 winner.
Sofia Kenin, another seed, staged a remarkable first-set turnaround to ensure she remained in the competition.
The American trailed 5-2 in the opener but rallied to defeat Jasmine Paolini 7-5 6-1.
Defeats Paolini 7-5, 6-1 pic.twitter.com/5F0gnzmVzg
— WTA (@WTA) September 19, 2019
Former US Open winner Sam Stosur came through 6-2 7-6 (7-1) against Nina Stojanovic, while Anna Blinkova defeated Marie Bouzkova, who had ousted Elina Svitolina.
At the Korea Open, Priscilla Hon stunned Australian compatriot and 2018 runner-up Ajla Tomljanovic in a 6-3 5-7 6-1 win.
The 21-year-old qualifier was playing Tomljanovic for the first time.
Karolina Muchova eased past Timea Babos, as Paula Badosa saw off Patricia Maria Tig.