Webb lost to Grace Park 1-up while Diaz never recovered from a quick start by Hee-Won Han to fall 3-and-2.
The 32-player field featured 16 players from the LPGA Tour and 16 players from the Japan LPGA Tour (JLPGA). The players were ranked by their current position on each tour's money list and the top players from the LPGA met the bottom players from the JLPGA and vice versa.
American Rosie Jones trounced Chieko Amanuma 5 and 4 in the second round's first match. Amanuma may have been suffering from a big-win hangover after beating the world's top player, Annika Sorenstam, in the first round.
Midori Yoneyama edged out a 1-up victory over Lorie Kane after Kane blew a 2-up lead in the latter stages of their match. Yoneyama won three of the last four holes to advance into the quarterfinals against Kelly Robbins.
Robbins lost only one hole Friday when she bettered fellow American and Solheim Cup teammate Cristie Kerr, 2-up.
Michele Redman dispatched Takayo Bandoh 4-and-3 as Bandoh's magical run ended quickly. She bested Se Ri Pak in Thursday's first-round match-up.
Carin Koch destroyed Catriona Matthew 5-and-3 and will face Redman in the quarterfinals.
Yuri Fudoh defeated Rachel Teske 3-and-1 in the final second-round match. Teske came out Friday to finish her first-round match against Yu-Chen Huang as the two were forced to stop Thursday because of darkness. Teske needed only one hole Friday to oust Huang but ran into trouble against Fudoh.
Webb and Park each won two holes on the front side to make the turn all square. Webb won the 11th but Park went on a tear with three wins in the next four holes to go 2-up.
Webb won the par-5 17th to get to 1-down but the players halved 18 and Park advanced to the quarterfinals to meet Fudoh.
Han jumped out of the gate with wins at the second and fourth holes. Diaz answered with a win at the fifth but Han responded with a victory at the sixth to reclaim her 2-up lead.
Han captured the ninth and 11th holes to go 4-up but Diaz fought back with a win at No. 15. When the pair halved 16, Han had her 3-and-2 win and will meet Jones in Saturday's first quarterfinal match.
Results from the Cisco World Ladies Match Play Championship