Andy Murray (Photo: Reuters)
Top ranked Serena overcame a slow start to turn away Japan's Ayumi Morita 6-3 6-3 in third round play, but Venus was forced to withdraw from the tournament with a back injury.
Murray, meanwhile, needed only 56 minutes to defeat sluggish Australian Tomic 6-3 6-1 in his second round match.
"I don't know if he was tired or struggling with the humidity, but he was playing pretty low percentage tennis," Murray told reporters. "With the conditions like they were today, that played into my hands."
The 2009 Miami champion won 80 percent of his first service points and broke Tomic twice in each set to improve to 2-0 all-time against the Australian.
Murray, runner-up to world number one Novak Djokovic last year, will face Bulgaria's Grigor Dimitrov in the third round. Dimitrov was leading 6-4 1-1 when Italy's Simone Bolelli was forced to retire.
Serena Williams, seeking a record sixth Miami title, fell 3-0 behind in the first set against her Japanese opponent but capitalized on four of her six break points to win.
The loss left Morita 0-19 against top 10 players, while Serena remained on course to break a tie with Steffi Graf for the most singles titles in the tournament.
Venus Williams, however, pulled out of the tournament with a lower back injury before her match with fellow American Sloane Stephens.
"This is just the kind of tournament you want to play well at," Venus said. "But I have faced disappointments in my life and my career. It's not the first and probably not the last."
Spanish wildcard Garbine Muguruza Blanco delivered the day's biggest stunner, eliminating ninth seed Caroline Wozniacki of Denmark 6-2 6-4 in 81 minutes.
Fifth seed Li Na of China, playing her first tournament since injuring her ankle in the Australian Open final, dismissed American Varvara Lepchenko 6-2 6-4.
Polish defending champion Agnieszka Radwanska collected a 7-6 2-6 6-3 win over Slovakia's Magdalena Rybarikova to advance to the fourth round.
In other men's second round play, Frenchmen Jo-Wilfried Tsonga and Richard Gasquet both won.
Tsonga defeated Serb Viktor Troicki 7-6 6-3, Gasquet turned back Belgium's Olivier Rochus 7-5 6-2 and American Sam Querrey beat Poland's Lukasz Kubot 4-6 6-3 6-3.
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