The 18-year-old sixth seed looked to be cruising to victory when she bagged the first set with an audacious backhand slice dropshot on her fourth set point against Frech.
The world number 25, however, was far from finished, breaking at the start of the second set with Andreeva losing her calm and hitting a ball high out of the court.
With Andreeva's composure rapidly eroding and her unforced error count shooting up, Frech levelled when the Russian teenager's slice forehand sailed long.
The Pole then powered past Andreeva with a bagel in the third, the first time Andreeva has lost a deciding set with a 6-0 scoreline in her professional career.
Lucky loser Ons Jabeur, beaten on Sunday in the last qualifying round, made the most of her unexpected chance with a 7-6 6-1 win over American Caroline Dolehide on Monday.
Jabeur, a two-time Wimbledon finalist, looked comfortable on grass ahead of the season's third grand slam.
The Tunisian, who has slipped to 61st in the world, earned a win for only the second time in her last five tournaments, and will come up against fourth seed Jasmine Paolini.
World No.9 Emma Navarro also advanced, with a comfortable 6-2 6-3 win over Ukraine's Marta Kostyuk.
She will next play eighth seed Paula Badosa after the Spaniard dispatched local hope Eva Lys 6-1 6-3 in 61 minutes.
Swiss underdog Rebeka Masarova caused a minor upset, eliminating former Australian Open champion Sofia Kenin of the United States 6-3 6-2 in a similar time.
In the Nottingham WTA 250 Queenslander Kim Birrell lost to Danish Mo.2 seed Clara Tauson 7-5 6-2.
