Fernley has enjoyed a meteorite growth in the last 12 months, which is now 60th in the world from outside the top 500.
It was just his sixth tour-level match on the grass, but it did not seem because he had played some great tennis many times, for which there was no answer.
The British number two came back from 0–40 in his first service game of two matches, before he broke the mattate to control the opener.
It looked like a direct afternoon for Fernley as Mutet had grown rapidly, but French withdrew its composition to dominate the second set, swinging after three double defects in her first service game by Scott in her first service game.
However, Fernley found an additional level in an excellent third set and Mutet had no response to his big hitting, boiling her frustrations, boiling that he obtained a time violation after arguing with the umpire.
But Fernley put his creation well to win the last eight and join the compatriot and British number one Jack Draper.
“I tried to stick to my game plan and be aggressive,” he said. “I did it better in the third set and the result speaks for myself.
“This is really special for everyone here and I have to see playing at this level.”