Mikael Ymer lost the first set in the round of 16 against the American Mackenzie McDonald, who is ranked 63rd in the world, with 3–6.
But the Swede came back and won the second set 7–6 and took home the match after 6–3 in the third set.
The match lasted for just over three hours.
In the quarter-finals, Mikael Ymer, who is ranked 77th in the world, faces Soonwoo Kwon from South Korea, who is ranked 84th in the world.
Earlier in the ATP tournament, the 24-year-old Swede won the Nordic meeting against Finnish Emil Ruusuvuori in the round of 16 with 6–4, 4–6, 6–3.
Ymer and Björklund lost in the qualifier
In the qualifiers for the Australian Open, Elias Ymer went out after losing 6–7, 6–7 in an even match against the Taiwanese Hsu Yu Hsiou.
Mirjam Björklund also went out in the second round of the qualifiers in Melbourne when she lost 1–6, 6–4, 6–7 against the Japanese Nao Hibino.
Mikael Ymer thus becomes the only Swede in the year's first grand slam tournament, which begins on Monday.