Moore, who has a 10,000-point lead over Fitzgibbon, will subsequent face Frenchwoman Johanne Defay after sending New Zealander Paige Hareb packing with 13.20 to 11.00 victory.
Defay edged Costa Rican Brisa Hennessy 10.66 to 9.54.
The opposite identify contender Peterson thrashed Silvana Lima 13.43 to eight.54 to arrange a quarter-final with Australian Nikki Van Dijk, who scored 12.40 to overcome American Courtney Conologue by way of 0.06 issues.
In the meantime, Gilmore narrowly edged compatriot Macy Callaghan 13.07 to 12.13 to guide a surf-off with American international No.five Caroline Marks, who knocked out Australian Bronte Macauley 12.67 to 9.83.
Within the males’s ultimate 16 heats, Wade Carmichael slumped 14.60 to 9.27 towards Brazilian identify contender Felipe Toledo.
The arena No.2’s victory over the Australian driven the identify race out to a showdown at Pipe Masters, the overall match of the excursion.
“I am in point of fact glad to push the identify out to Hawaii, I believe it is going to make issues much more fascinating for everybody,” Toledo stated.
The identify race used to be blown even additional open after reigning international champion and chief Gabriel Medina used to be disenchanted by way of fellow Brazilian Caio Ibelli.
Medina were main 14.34 to 7.17, however then in a second of bewilderment began paddling his opponent’s wave with out precedence.
He used to be sensationally docked all issues for his lower-scoring wave to deliver the rankings again to eight.17 to 7.17 and Ibelli then controlled to snatch a three.10 to knock a shell-shocked Medina out.
Ibelli stated there used to be a transparent confusion over the concern as Medina does not make mistake like that.
“I think like browsing sensible he received the warmth, however the whole thing went my manner. I’ve such a lot appreciate for him,” Ibelli stated. “I think so dangerous, I imply I did my recreation and I got here out with the win however he surfed lovely excellent.
South American Jordy Smith, Brazilian Italo Ferreira and American Kolohe Andino stay within the identify race in Portugal.
American 11-times international champion Kelly Slater used to be edged by way of Japan’s Kanoa Igarashi.