“Every time I walk on the court, I believe I can win, and I think I believed more this time than probably the last time I played her,” the 20-year-old Bouchard, beaten by Williams in three sets in their only previous meeting, told reporters.
“It’s always an opportunity for me to play someone I’ve watched on TV when I was younger and someone who’s been No. 1 and such a great player.
“So I always expect great tennis because she’s still playing at a great level, and she was at an amazing level.”
Williams, the 11th seed who won the tournament a decade ago but has struggled with health issues in recent years, felt her inconsistency had made the biggest difference against Bouchard after she had battled through her two previous matches.
“My errors really hurt me a lot today, just a lot of up and down, a lot of errors,” said the American. “(I didn’t) have the endurance this week, so I think that contributed to my errors.
“I just kind of wanted to make the points shorter a lot of the times. I made some bad choices or my legs would stop. So that kind of made it more challenging.”
Next up for Bouchard in the last eight is Serbia’s Jelena Jankovic, the second seed and 2007 champion, who shrugged off a close opening set to beat Croatia’s Ajla Tomljanovic 7-5 6-1.
In other matches on Thursday, Germany’s 2009 champion Sabine Lisicki, the fourth seed, was knocked out by compatriot Andrea Petkovic 6-1 6-0, while Swiss qualifier Belinda Bencic fought back to beat Ukrainian teenager Elina Svitolina 6-7(4) 6-4 6-1.
Third-seeded Italian Sara Errani scraped past China’s Peng Shuai 7-6(6) 7-6(5), Slovakia’s Daniela Hantuchova brushed aside Brazil’s Teliana Pereira 6-2 6-3 and Jana Cepelova, also of Slovakia, fended off Russian Elena Vesnina 7-6(4) 3-6 6-3.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Peter Rutherford)