Sharapova, who won the title last week at Indian Wells, will next take on Czech Klara Zakopalova for a quarter-final.
The Russian star has never won the Miami title, although she’s reached the final four times.
In hot, humid, windy weather, Vesnina started strong, breaking Sharapova to take a 3-1 lead in the opening set. Sharapova responded by winning 11 of the next 14 games to secure a straight-sets victory.
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