The world number one and top seed, defending champion at the premier clay event in the Spanish capital, needed just over an hour to dismiss the 13th-seeded Russian and set up a last-eight meeting with Spanish wildcard Anabel Medina Garrigues.
"I just felt really relaxed today," Williams said. "I felt like I was just taking my time. So hopefully I can keep calm and relaxed."
Williams, 31, chasing a fourth title of the year and the 50th of her career, was joined in the quarter-finals by second seed Maria Sharapova who knocked out unseeded German Sabine Lisicki 6-2 7-5.
The Russian world number two and French Open champion will play Kaia Kanepi for a place in the last four after the unseeded Estonian beat Slovakian wildcard Daniela Hantuchova 6-3 6-4.
Medina Garrigues, a former world number 16 now ranked 63rd, went through on Wednesday after her opponent Yaroslava Shvedova of Kazakhstan withdrew with an arm injury.
"She's definitely going to be really tough for me," Williams said of the Spaniard. "She's a grinder on clay and she's Spanish. I know a lot of fans really like her here."
After her comfortable win over Lisicki, Sharapova reflected on how much she has improved on clay in recent years.
The 26-year-old's triumph at Roland Garros in 2012 made her only the sixth woman in the open era to win all four Grand Slam singles titles.
"It took me many years to get to the level of where I am today (on clay), it certainly didn't happen overnight," she said.
"I worked extremely hard on getting stronger and recovering better, moving better on the court, giving myself a better position on the court, especially after being on the defensive and trying to play aggressively as I always do on quicker surfaces.
"But just give myself that chance to recover. I think I've learned a lot and over the years and I've really improved."
The other two quarter-finals feature Italian seventh seed Sara Errani against unseeded Russian Ekaterina Makarova and sixth seed Angelique Kerber of Germany against Serbian 16th seed Ana Ivanovic.
WTA Madrid Open round three matches
1-Serena Williams (US) beat 13-Maria Kirilenko (Russia) 6-3 6-1
2-Maria Sharapova (Russia) beat Sabine Lisicki (Germany) 6-2 7-5
Anabel Medina Garrigues (Spain) beat Yaroslava Shvedova (Kazakhstan)WO
Kaia Kanepi (Estonia) beat Daniela Hantuchova (Slovakia) 6-3 6-4
Ekaterina Makarova (Russia) beat 14-Marion Bartoli (France) 6-3 6-2
7-Sara Errani (Italy) beat Varvara Lepchenko (US) 7-5 6-3