The Czech lefty was an unseeded finalist at Roland-Garros two years ago and lost in the first round to eventual champion Iga Swiatek upon her return to Paris last September.
She booked her place in the round of 16 to face Badosa with a 6-3, 6-3 win over Slovenian Polona Hercog.
"Badosa is playing great on clay, especially this year, so it's gonna be tough," Vondrousova said in her post-match press conference.
Carreno Busta returns to the last 16
In their first meeting at a Grand Slam, No.12 seed Pablo Carreno Busta was looking to book a last-16 place at Roland-Garros for the third time when he came up against Steve Johnson.
The American world No.88 was seeking his first fourth-round appearance in Paris, but it wasn't to be. Despite strong returning from Johnson, Carreno Busta eased through 6-4, 6-4, 6-2.
"I suffered a little bit at the end of the second set, but, well, the feeling on court was very good," admitted Carreno Busta, a quarter-finalist in the French capital last year. "I feel very comfortable. Well, very happy to be again in the fourth round."