Vondrousova won her first tour title hours after the 36-year-old Francesca Schiavone was the other WTA tournament winner in Bogota, Colombia.
Schiavone played in WTA events in her native Italy before Vondrousova was born in June 1999.
The 233rd-ranked Czech clinched the first edition of the Swiss indoor hard-court tournament when Kontaveit netted a forehand under pressure from another powerful ground stroke.
Vondrousova did not drop a set in the main draw after advancing through three rounds of qualifying. She beat top-seeded fellow Czech Barbora Strykova in the semifinals to reach her first final on tour.
On Sunday, the left-handed Vondrousova overcame double-fault problems on her serve to save 13 of the 14 break-point chances that 99th-ranked Kontaveit had. Vondrousova also saved the two set points she faced in the second-set tiebreaker.
Vondrousova now moves on to play in the United States next weekend. She is in the Czech squad for the defending champion's Fed Cup semifinal against the U.S. at the Saddlebrook Resort, Florida.