The 18-year-old overcame a woeful first set to grow into the match. And after failing to serve it out at 6-5 in the decider, she got the job done when the chance next arose to go through 2-6, 6-3, 11-9 in exactly three hours.
With Heather Watson through yesterday it is the first time since the 1991 US Open that Britain has two women in the last 32 of a Grand Slam event.
Robson, who faces American Sloane Stephens next, said: "I thought the game was pretty ugly but in terms of how tough it was to close it out at the end it was right up there with my best.
"I never gave up, even when she went up a break twice in the third. I thought I had to get as many returns in as I could and in the end I had nothing to lose. So I relaxed on my serve and decided to go for it.
"In the first set it was just too up and down. You can't win a set when you are hitting five unforced errors to every winner.
"At the start of the second I knew I had to play with more consistency.
"In some matches you lose some belief but in this one I always felt I could win."