The 28-year-old Keys began the match in typically aggressive fashion, firing off powerful returns and groundstrokes to break serve and go 2-0 ahead.
The breaker seemed to take the wind out of Andreeva's sails.
Keys stormed into an early 2-0 lead in the third set after the Russian double faulted in her opening service game, before finishing off her opponent in a shade over two hours.
In her second quarter-final at Wimbledon, Keys will face either second-seeded Belarusian Aryna Sabalenka or another Russian in Ekaterina Alexandrova, the 21st seed.
Reporting by Aadi Nair in Bengaluru; Editing by Ken FerrisOur Standards: The Thomson Reuters Trust Principles.
Persons:
Madison Keys, Russia's Mirra Andreeva, Toby Melville LONDON, Anna Kournikova, Keys, groundstrokes, Andreeva, Ekaterina Alexandrova, Aadi Nair, Ken Ferris
Organizations:
Lawn Tennis, Croquet Club, Madison, Wimbledon, Thomson
Locations:
London, Britain, Russian, Bengaluru