World number one Serena beat 24th seeded Russian Svetlana Kuznetsova 6-2 6-3 producing 29 winners and 20 unforced errors.
Kuzentsova, who owns two grand slam titles, had beaten Serena twice in their previous nine meetings but the outcome of this contest never looked in doubt.
"I know Svetlana is super tough and we always have super tough matches," said Serena.
"It seems like I'm cruising but don't think I'm cruising. I have my matches and I'm really focused in my matches because all these players I play are really good," she added.
Serena has now won 18 straight matches and she is looking to add to her seven titles in Miami with her third straight triumph after winning in 2013 and 2014.
Venus continued a winning streak of her own -- making it seven wins in seven against fellow former world number one Caroline Wozniacki with a 6-3 7-6(1) victory.
The win also made it seven wins in her last eight against top 10 opponents, highlighting Venus's return to form after her health problems.
The older Williams sister will face Carla Suarez Navarro in the last eight following the Spaniard's win over seventh seed Agnieszka Radwanska 5-7 6-0 6-4.
Romanian third seed Simona Halep won through after beating Italy's Flavia Pennetta 6-3 7-5. - Reuters
