Stephens broke through for her first win of 2020 to book her spot in the second-round match following a difficult start to the year.
But the American fifth seed was upstaged by 17-year-old Fernandez, who rallied past the 2017 US Open champion in three sets midweek.
Fernandez was a surprise finalist at last week's Mexican Open in Acapulco, where the Canadian reached her maiden WTA decider.
The in-form teenager moved through to back-to-back quarter-finals after prevailing in more than two hours against Stephens, with either top seed Elina Svitolina or Olga Govortsova awaiting.
Elsewhere at the WTA International event, sixth seed Rebecca Peterson defeated Kateryna Bondarenko 7-6 (7-2) 7-5, seventh seed Wang Yafan outlasted Astra Sharma 7-6 (7-5) 4-6 6-3 and ninth seed Marie Bouzkova beat Anna Karolina Schmiedlova 6-4 6-1.