The 20-year-old Vikhlyantseva, another promising talent, was outplayed in the opening set but after breaking to take a 3-1 lead in the second, Kontaveit moved into overdrive to halt the comeback swiftly and win the next five games.
The victory will shoot the young prospect from Tallinn from world number 49 to a new career-high of 36 when the rankings are announced on Monday.
The men's final between two veterans, 34-year-old Gilles Muller and 38-year-old Ivo Karlovic, was being played later on Sunday.
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(Reporting by Ian Chadband; Editing by Toby Davis)
