Tauson is seeded tenth in the tournament. Ruzic, who is ranked 78th in the world, was unseeded. In her next match, Tauson will face either seventh-seeded Jasmine Paolini of Italy or world no. 109 Yue Yuan from the host nation.
Tauson began brightly and seemed on top until 3-2, when Ruzic broke back.
The first serve was a challenge for Tauson throughout the set, but Ruzic had the same problems in a first set, rich with unforced errors.
Tauson immediately took a 4-3 lead, and although she missed two set points at 5-3, she served out the set soon after.
The first set win seemed to give the Dane more peace of mind. She started playing with greater stability and seemed more liberated in her style of play.
Tauson also seemed to handle the intense heat quite well. In the match before, Karolina Muchova had thrown away a 5-3 lead in the first set and was trailing 1-4 in the second when she retired feeling uncomfortable in the challenging conditions.
Mentally, Tauson was on top, which probably also made it easier to forget the oppressive heat.
Ruzic's frequent winning shots from the first set were completely gone, and Clara Tauson cruised to a rock-solid victory.