The 25-year-old Russian moved a step closer to her first title on tour with a comprehensive 6-2 6-4 triumph at the WTA International clay-court event on Thursday.
Panova flew out of the blocks and dropped just six points in winning the opening four games, winning 65 per cent of points on Min's serve in the first set.
A nervy start to the second set saw four consecutive breaks before both players found their rhythm, but, with the score at 4-4, Min was unable to stop Panova pushing ahead.
The world number 137 wasted two break points and a match point before securing her progression in an hour and 15 minutes.
She will meet Silvia Soler-Espinosa in the last eight after the Spaniard came from a set down to beat Julia Goerges 4-6 6-1 6-3.
After suffering three breaks in the opening set, Soler-Espinosa won five games in a row to win the second and did not look back from there.
Mona Barthel's hopes of a third career win remain intact after she sealed her last-eight spot with a 6-4 3-6 6-4 victory over Gabriela Dabrowski.
Barthel, who reached the semi-finals in Sweden two years ago, needed two hours and 32 minutes to see off the challenge of her Canadian opponent and will meet Kaia Kanepi next after her 6-3 6-1 win over Richel Hogenkamp.