The American star dispatched Italian Roberta Vinci 6-2, 6-1 in 67 minutes as she continued her quest for a sixth Miami championship after returning from a seven-week injury absence.
Sharapova, meanwhile, had little trouble with American qualifier Sloane Stephens, besting her 6-4, 6-2.
The three-time Miami runner-up now goes on to face fellow Russian Ekaterina Makarova, who breezed by German Mona Barthel 6-2, 6-4.
Not so fortunate, however, was Kim Clijsters, who came up short against 23rd-seeded fellow Belgian Yanina Wickmayer. The latter posted a 6-4, 7-6 (7-5), victory to move on.
China's Li Na, seeded eighth, also advanced with a 7-5, 6-2 decision over Czech Iveta Benesova. She'll face 12th-seeded German Sabine Lisicki, who dismissed Peng Shuai of China 7-5, 6-2.
Celebrity Families of 2014 [PHOTOS]