The 19-year-old world number 38 dominated from start to finish as Sevastova made 24 unforced errors and managed just seven winners in the 59-minute encounter.
Vondrousova, one of three teenagers alongside Amanda Anisimova and Iga Swiatek in the second week at Roland Garros, will face either Estonia's Kaia Kanepi or Croatian 31st seed Petra Martic in the last eight.
"She's a great player but I played my best tennis today and I'm really happy," said Vondrousova, who also reached the US Open fourth round last year and won the junior doubles in Paris four years ago.
"It was my first junior Grand Slam so I'm in love with this place and I'm enjoying playing here."
Results from the eighth day of the French Open on Sunday (x denotes seeding):
Stan Wawrinka (SUI x24) bt Stefanos Tsitsipas (GRE x6) 7-6 (8/6), 5-7, 6-4, 3-6, 8-6
Roger Federer (SUI x3) bt Leonardo Mayer (ARG) 6-2, 6-3, 6-3
Kei Nishikori (JPN x7) leads Benoit Paire (FRA) 6-2, 6-7 (8/10), 6-2 - match suspended due to darkness
Rafael Nadal (ESP x2) bt Juan Ignacio Londero (ARG) 6-2, 6-3, 6-3
Sloane Stephens (USA x7) bt Garbine Muguruza (ESP x19) 6-4, 6-3
Johanna Konta (GBR x26) bt Donna Vekic (CRO x23) 6-2, 6-4
Marketa Vondrousova (CZE) bt Anastasija Sevastova (LAT x12) 6-2, 6-0
Petra Martic (CRO x31) bt Kaia Kanepi (EST) 5-7, 6-2, 6-4