Britain's Raducanu, the 2021 US Open champion, converted her seventh match point to beat China's number eight seed Yuan Yue 6-4, 6-3 in the last 16 in Seoul.
The 21-year-old Raducanu, ranked 70th in the world, has struggled with injuries since her stunning US Open victory and has failed to build on her success.
But she said she was pleased to come through another "good physical test" in humid conditions as she prepares to face world number 13 Kasatkina on Friday.
"Especially after not having played a lot of matches, to be able to churn out that kind of level twice now, having to back it up tomorrow and the next day without a day off, I'm looking forward to the challenge," said Raducanu, who beat American Peyton Stearns in her opening match in the South Korean capital.
"I trust my body a lot more now."
Raducanu is looking to make an impact at the Korea Open, which has been hit by a string of last-minute withdrawals including world number one Iga Swiatek, US Open runner-up Jessica Pegula and former Wimbledon champion Elena Rybakina.
Kasatkina moved into the quarter-finals with a 6-4, 6-2 win over American Hailey Baptiste.
"For me, it's going to be a big challenge physically and tennis-wise, but at the same time I don't have anything to lose," said Raducanu.
"She's expected to win but I know how dangerous I am and I think I'm improving match to match."
Raducanu took a medical time-out to get her foot strapped in the first set against Yuan, last year's beaten finalist.
She came back to close out the first set and raced into the lead in the second, but needed to dig in to finish off her stubborn opponent.
"I think the key to my success today was trying to let go of any frustration that happened," said Raducanu.
"Closing out the match I had a lot of match points I couldn't convert, so just staying focused and breaking in that last game."
Joining Raducanu in the quarter-finals is number-three seed Beatriz Haddad Maia of Brazil, who beat Australia's Ajla Tomljanovic 6-3, 6-4.
Bulgaria's Viktoriya Tomova also progressed after American opponent Amanda Anisimova retired while 7-5, 4-1 down in the second set.
Anisimova took a medical time-out after struggling with the heat and was visibly distressed in the break between sets.
