The third seed outclassed her compatriot 6-4 6-2 in an hour and 47 minutes to keep her strong recent form going.
Next up for Sharapova is Klara Zakopalova, the Czech 21st seed, who hopes to take two consecutive Russian scalps after dumping out 14th seed Maria Kirilenko 6-2 7-6.
But the French Open champion will be competing knowing she has a chance to reclaim the world number one ranking from Serena Williams in a city she loves, but one which has seen her lose four finals including the last two.
Sharapova said: "I personally love Miami, I've been coming here since I was a little girl.
"I've only had a few days to recover from Indian Wells but there's no greater motivation than winning."
Round three results
8-Sara Errani (Italy) beat Simona Halep (Romania) 6-1 6-0
12-Ana Ivanovic (Serbia) beat Svetlana Kuznetsova (Russia) 6-3 6-3
15-Roberta Vinci (Italy) beat 20-Carla Suarez Navarro (Spain) 5-7 6-4 6-4
3-Maria Sharapova (Russia) beat 29-Elena Vesnina (Russia) 6-4 6-2
21-Klara Zakopalova (Czech Republic) beat 14-Maria Kirilenko (Russia) 6-2 7-6(4)
28-Sorana Cirstea (Romania) beat 6-Angelique Kerber (Germany) 6-4 6-0
32-Alize Cornet (France) beat Lauren Davis (U.S.) 2-6 6-3 6-2
22-Jelena Jankovic (Serbia) beat 11-Nadia Petrova (Russia) 7-6(7) 6-4