The 19-year-old, who celebrated her birthday on Monday, beat the fifth-seeded Ukrainian 6-3 3-6 7-6 to become the youngest US Open semifinalist since Maria Sharapova in 2005.
Victory over Svitolina is another feather in the cap for Fernandez in this incredible run, with the Canadian already dispatching reigning champion Naomi Osaka and 2016 winner Angelique
"Today's match was definitely one of the hardest, not only tennis-wise, but also mentally and emotionally," Fernandez told reporters.
"Svitolina is a great player, great fighter. I was glad I was able to fight in the first set. In the second set, she upped her level, and I unfortunately made a few mistakes on key moments.
"I'm glad I was able to recuperate for the third set. The tiebreaker, too. A little bit lucky at five-all, but I'll take all the luck I can get. I was glad I was able to push through the finish line."
Fernandez has become a fan favorite at Flushing Meadows during her run and the supporters inside Arthur Ashe were once again audibly getting behind her.
The youngster showed remarkable poise for someone so inexperienced in what was a tense match, winning the final two points -- the first of which was a somewhat fortuitous net cord -- in the deciding tie break.
When she got back to the locker room, Fernandez said the first thing she did was call her dad.
"He honestly told me that I put him through hell and back with this match," she laughed.
"But he's very happy for me. He's glad that I was able to fight for every point, I deserved this win. Just keep working, enjoy this win today, and tomorrow we'll go back to work."