During the 90-minute delay, Ruse pulled the plug on her effort, sending ninth seed Eala through.
Eala, the emerging WTA star who captured her first WTA title in Washington this month, will next play Amanda Anisimova after the American ninth seed beat Turk Zeynep Sonmez 6-2, 6-3.
As always, world number 20 Eala was supported by a vocal crowd of compatriots, with Philippines flags displayed in abundance.
The 21-year-old has enjoyed similar support around the world -- in her run to the second week of Wimbledon, her breakthrough win in Washington and at this months' 1000 event in Toronto, where she was beaten in the fourth round by Swiss veteran Belinda Bencic.
Eala and Ruse swapped breaks in the first two games before Eala ran off six straight games to pocket the set.
They got through three more games in the second before the weather threat sent them indoors.