Eala, 21, defeated the seventh seed from Canada 6-2, 7-6(1) for a place in the WTA Tour tournament's last eight, battling back from 5-1 down in an epic second set.
It continues a breakout season for Eala, who last month made global headlines beating Iga Swiatek at Wimbledon to become the first Philippines player to reach the last 16 of a Grand Slam, and has soared to 28th in the world rankings.
Eala took the first set 6-2, exploiting multiple unforced errors from Fernandez. The roles reversed early in the second set, which Fernandez led 5-1.
But Eala battled back to lead 6-5 before Fernandez finally held serve to force a tie-break.
Eala stormed into a 3-0 tie-break lead. Fernandez gained a foothold after a long rally, but Eala's stunning cross-court forehand gave her five match points. She only required one.
"Everything's kind of a blur right now. I really made an effort to stay in the moment, and I was ready for anything that could have happened," said Eala.
"And luckily -- well, it wasn't a lot of luck -- but luckily it went my way."
Fernandez had beaten Eala in straight sets in Stuttgart earlier this year.
Victory meant Eala reaches her fifth quarter-final of a superb season, with either second-seeded Ukrainian Elina Svitolina or Uzbekistan's Polina Kudermetova awaiting in the next round.
Eala has been tipped to become a star of the women's game since defeating Swiatek to reach the Miami Open semi-finals last year, and stoked that hype further with her recent Wimbledon run.
She enjoys huge support from her native Philippines, where she is already the Southeast Asian nation's biggest female sports star in recent years.
On Tuesday in Washington DC, Eala rallied to defeat China's Zheng Qinwen 4-6, 6-4, 6-1 after 2hr 26min.
