Robson came into this week ranked a career-high No.54, with results in recent months including a runner-up showing in Guangzhou, a semifinal appearance in Palermo and a run to the fourth round at the US Open.
The eighth-seeded Robson's 64 64 second round win over Zhou Yi-Miao here featured a bizarre first set in which she cruised to a 5-0 lead, lost four straight games and then held at love by closing the set with an ace.
"I was playing aggressive and not missing very much and then at 5-0 I just lost my concentration a little bit and allowed her back into the match," Robson said. "She started getting a little bit more confidence and was going for her shots more. I'm a little bit disappointed with the way that I played today. I wasn't aggressive enough."
Nevertheless, the 18-year-old Robson has now won 10 of her last 13 main draw matches. Next up for her is Chang Kai-Chen.
"I've played doubles with her before," Robson said. "I think I know her pretty well. She's tough to play against. She plays really fast and moves really well. It's going to be a tough match for sure."
Fellow Brit Heather Watson also advanced, 67(4) 62 63, over No.6 seed Anabel Medina Garrigues. Watson rallied from 5-3 down in the first set to take a 6-5 lead, but couldn't hang on. Nevertheless, she pulled out the victory.
"I knew it was going to be a tough match today," Watson said. "Anabel is a great player, has a lot of experience and she makes a lot of balls. I knew I was going to have to win the points and she wasn't going to give me anything.
"The first set was very close. It was a high-quality, good set. She played well to win it. I was obviously disappointed, but she earned it. So I just thought, 'I'm playing well. I'll come back in the second set. And stay positive.' And it ended up working today."
This will be the first time since February 2010 in Memphis that a WTA final eight will contain two Brits.
"I think it's good when we see each other doing well because it pushes the other girl to do just as well," Watson said of Robson. "We're good friends off the court. We have a healthy rivalry. We're pushing each other along. I think British tennis is looking good."
Watson's showdown against Pauline Parmentier will be her fourth career quarterfinal and first this year, but she has yet to win one. Parmentier was a surprise 63 64 winner over second-seeded Zheng Jie.
Friday's other two matches will see No.1 seed and 2009 Osaka champion Samantha Stosur play Jamie Hampton and No.7 seed Chanelle Scheepers take on Misaki Doi in the South African's fourth quarterfinal of the season.
Among those reaching the doubles semifinals were top-seeded Raquel Kops-Jones and Abigail Spears. The Americans are trying to catch up to Maria Kirilenko and Nadia Petrova for the fourth and final spot remaining in the draw at the TEB BNP Paribas WTA Championships - Istanbul 2012.