Raducanu dropped her first set to the 17-year-old from the Czech Republic, but bounced back to win the second and third despite a lengthy suspension due to rain.
The 78th ranked Brit finished on top 4-6 6-4 6-2 against the relatively evenly matched Fruhvirtova, who is only one rank behind.
Raducanu will face 24-year-old Viktoria Kuzmova from the Slovak Republic in the round of 16.
Talking about her goals for the season, Raducanu admitted that fitness was at the top of the list.
"For 2023 my goal is to stay healthy for longer," she said.
"I'm looking forward to working hard because I've got a better idea of what to expect now. So I'll be less like a deer in the headlights.
"For a results goal I'd say it's to win a title, and three I'd say is to be playing fearless tennis. Just not thinking about consequences. Just going for it."