Both players struggled to deal with the conditions in the early stages of the match, but neither could be separated in the opening five games as the tie remained on serve.
Vesnina took control in the latter stages of the first set, however, breaking at 2-3 before another break of serve allowed the Russian to claim the opener in just over 40 minutes of tennis.
The wind continued to cause havoc in the early stages of the second, but it did nothing to quell Vesnina's dominance as the Russian's impressive first serve continued to cause Hampton concern.
Another break of serve allowed Vesnina to move into a 2-0 lead, before a hold moved her into a 3-0 lead in the second.
Hampton did move onto the board in her next service game, but Vesnina continued to dominate from the baseline as she broke once more before serving for her second title.