The Belgian progressed to her maiden grand slam quarter-finals in her first appearance in the Australian Open main draw, beating Croatian Petra Martic 7-6 (5) 7-5.
In the fourth round she confidently beat Czech Denisa Allertova with the score 6: 3, 6: 0.
Mertens missed last year's Australian Open after qualifying for the Hobart International and winning the tournament, meaning she wasn't able to make qualifying for the first grand slam of the year.
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Martic forced a tiebreak and was trailing 2-3 when Mertens switched gears, eventually clinching the opening set with a sharp forehand victor. "I played my game today and tried to stay aggressive".
This is a hard match to call, for neither of these players regularly have long runs at Grand Slams.
Asked how much she learned, Kostyuk said: "A lot".
"He's by my side all the time".
Mertens made all the initial running, returning aggressively and mixing up her game cleverly, taking every opportunity to approach the net and cut off Svitolina's passing avenues. She struck 17 winners in 15 games, sealed 56% of the points on the opponent's first serve (23 of 41 points) and 13 of the 18 points behind the Czech's second serve.
Mertens, who for the past three years has trained at Clijsters' academy in Belgium with coach Robbe Ceyssens, led 4-0 in the first set before being taken to a tiebreak. Svitolina hasn't lost since the start of the season and dropped just a set this tournament.
Another break followed, and a third courtesy of a sumptuous backhand pass took Mertens to the brink of the last four at 5-0.
Kostyuk, who had nine double faults on Friday, including on match point, received an entry into qualifying because of her junior girls' victory previous year at the Australian Open. The Slovakian can take heart from getting this far in a Grand Slam, but she is going to have to replicate some of the form that saw her reach the semi-finals at Wimbledon past year, if she is to make this a contest.
"Kim, thanks for watching and don't get too stressed".